// Numbas version: exam_results_page_options
{"name": "QM Final Exam 2019-2020", "metadata": {"description": "<p>The assessment has been designed to take no more than 2 hours to complete. You must submit the test by 10:00 am (UK time) on 13th May. Once you start the test, it has to be completed by 2 hours.</p><p>When answering the exam you should observe normal exam conditions and must not communicate/collude with other students taking the paper. The work that you submit must be your own work. Should you encounter IT di\ufb03culties that signi\ufb01cantly a\ufb00ect your ability to complete this exam or when uploading your answer(s) you may submit a PEC detailing these.&nbsp;<br></p>", "licence": "None specified"}, "duration": 7200, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-shuffled", "pickQuestions": 1, "questions": [{"name": "Decision Making", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Shihan Miah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4456/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A car manufacturer company is facing increased competition. The company identifies three options to increase profit.</p>\n<ul start=\"4\">\n<li>Invest heavily in a marketing campaign</li>\n<li>Hire a new technology engineer</li>\n<li>Diversify and sell motor services as well as cars</li>\n</ul>\n<p>&nbsp;If the company take action it is anticipated that sales could improve in the next year by 10%, 20% or 30% depending on market conditions. The profit which can be expected depends on the level of sales and is shown in the table below.</p>\n<p>Table 1: expected profit</p>\n<table>\n<tbody>\n<tr>\n<td width=\"154\">\n<p>&nbsp;</p>\n</td>\n<td width=\"142\">\n<p>Sales improve by 10%</p>\n</td>\n<td width=\"142\">\n<p>Sales improve by 20%</p>\n</td>\n<td width=\"142\">\n<p>Sales improve by 30%</p>\n</td>\n</tr>\n<tr>\n<td width=\"154\">\n<p>Invest in marketing</p>\n</td>\n<td width=\"142\">\n<p>10,000</p>\n</td>\n<td width=\"142\">\n<p>15,000</p>\n</td>\n<td width=\"142\">\n<p>20,000</p>\n</td>\n</tr>\n<tr>\n<td width=\"154\">\n<p>Hire new engineer</p>\n</td>\n<td width=\"142\">\n<p>11,000</p>\n</td>\n<td width=\"142\">\n<p>20,000</p>\n</td>\n<td width=\"142\">\n<p>30,000</p>\n</td>\n</tr>\n<tr>\n<td width=\"154\">\n<p>Diversify</p>\n</td>\n<td width=\"142\">\n<p>-6,000</p>\n</td>\n<td width=\"142\">\n<p>30,000</p>\n</td>\n<td width=\"142\">\n<p>42,000</p>\n</td>\n</tr>\n</tbody>\n</table>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the best decision using the Maximax rule?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["Invest in marketing", "Hire a new engineer", "Diversity"], "matrix": [0, 0, "2"], "distractors": ["", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the best decision based on the Minimax Regret Rule?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["Invest in marketing", "Hire a new engineer", "Diversify"], "matrix": [0, "4", 0], "distractors": ["", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>The CEO decides to use a Hurwicz criterion of 0.3 to make the decision. Which is the best decision based on this criterion?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["Invest in marketing", "Hire a new engineer", "Diversify"], "matrix": [0, 0, "4"], "distractors": ["", "", ""]}]}, {"name": "Probability", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Shihan Miah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4456/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A coffee shop chain would like to reduce costs by introducing a new cheaper blend of coffee, but before they make the change, they decide to test how many customers will notice the difference. They test the new blend in two locations; Birmingham and Southampton. 2000 customers took part in the survey. 800 from Birmingham and 1200 from Southampton.</p>\n<p>96 of the customers in Birmingham answered &lsquo;Yes I can taste the difference&rsquo;.</p>\n<p>240 of the customers in Southampton answered &lsquo;Yes I can taste the difference&rsquo;.</p>", "advice": "<p>Provide your answers to 3 decimal places.</p>", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Determine the probability that a customer will not taste the difference. Give your answer to (3 decimal places).</p>", "minValue": "0.831", "maxValue": "0.833", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "5", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Given that a customer answers &lsquo;yes I can taste the difference&rsquo; what is the probability that they are from Birmingham?&nbsp;Give your answer to (3 decimal places).</p>", "minValue": "0.285", "maxValue": "0.287", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>The coffee shop believes that only 5% of customer will switch to a competitor if they introduce the cheaper coffee blend. The coffee shop chain take a sample of 50 customers.</p>\n<p>Calculate the probability that exactly 4 customers in this sample state that they will switch to a competitor.&nbsp;Give your answer to (3 decimal places).</p>", "minValue": "0.135", "maxValue": "0.137", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>State which probability distribution you used in part c).</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["Normal Distribution", "Binomial Distribution", "Poisson Distribution"], "matrix": [0, "2", 0], "distractors": ["", "", ""]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>State two assumptions of that distribution.</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": false, "choices": ["Two potential outcomes for each trial", "Probability of success for each outcome is same", "Number of trial is not fixed", "Probability of success and failure for each outcomes are equaly likely"], "matrix": ["1", "1", 0, 0], "distractors": ["", "", "", ""]}]}, {"name": "Normal Distribution", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Shihan Miah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4456/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Research shows that many customers will only wait for up to four seconds for an e-commerce website to display images before giving up and moving to a different website. This customer behaviour costs businesses huge amounts of money each year.</p>\n<p>Research has found that the mean time for e-commerce websites to display images is 8.57 seconds with a standard deviation of 1.80 seconds. The display times for the websites are normally distributed.</p>", "advice": "<p>Give your answers to 4 decimal places.</p>", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the probability that a website will take less than 4 seconds to display images?&nbsp;Give your answer to (4 decimal places).</p>", "minValue": "0.0054", "maxValue": "0.0056", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the probability that a website will take between 4 seconds and 7 seconds to display images?&nbsp;Give your answer to (4 decimal places).</p>", "minValue": "0.186", "maxValue": "0.187", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A display time of less than 4 seconds would be ideal. In a sample of 2000 websites, how many could be expected to load in less than 4 seconds?</p>", "minValue": "11", "maxValue": "11", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The CEO of a website design company believes that his company creates websites capable of displaying images faster than his competitor&rsquo;s websites. He takes a sample of 30 websites designed by his company. The mean time for the sample (was 6.1 seconds with a sample standard deviation of 1.2 seconds.</p>\n<p>&nbsp;</p>\n<p>What is the 95% confidence interval for the true mean time for websites designed by this company to display images.</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["[5.671,6.529]", "[5.723,6.832]", "[5.125,6.923]", "[5.651,6.629]"], "matrix": ["4", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Correlation and Regression", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Shihan Miah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4456/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>The following table gives information on the amount of ice-cream sold (by weight) in a city centre caf&eacute; and the temperature (in degrees Fahrenheit) in the city. The data was collected on 8 random days.</p>\n<p>Table 2: Temperature and ice-cream sold</p>\n<table width=\"589\">\n<tbody>\n<tr>\n<td width=\"145\">\n<p>Temperature (<sup>o</sup>F)</p>\n</td>\n<td width=\"56\">\n<p>93</p>\n</td>\n<td width=\"56\">\n<p>86</p>\n</td>\n<td width=\"56\">\n<p>77</p>\n</td>\n<td width=\"56\">\n<p>89</p>\n</td>\n<td width=\"56\">\n<p>98</p>\n</td>\n<td width=\"56\">\n<p>102</p>\n</td>\n<td width=\"56\">\n<p>87</p>\n</td>\n<td width=\"56\">\n<p>79</p>\n</td>\n</tr>\n<tr>\n<td width=\"145\">\n<p>Sales of Ice-cream (in kg)</p>\n</td>\n<td width=\"56\">\n<p>95</p>\n</td>\n<td width=\"56\">\n<p>79</p>\n</td>\n<td width=\"56\">\n<p>56</p>\n</td>\n<td width=\"56\">\n<p>90</p>\n</td>\n<td width=\"56\">\n<p>105</p>\n</td>\n<td width=\"56\">\n<p>126</p>\n</td>\n<td width=\"56\">\n<p>72</p>\n</td>\n<td width=\"56\">\n<p>53</p>\n</td>\n</tr>\n</tbody>\n</table>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate&nbsp;S<sub>xx&nbsp; &nbsp;</sub>to 3 decimal places. <sub>&nbsp;</sub></p>", "minValue": "522.874", "maxValue": "522.876", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate S<sub>yy&nbsp;</sub>to 1 decimal place<sub>&nbsp;.</sub></p>", "minValue": "4273.5", "maxValue": "4274.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate S<sub>xy&nbsp;</sub>to 1 decimal place<sub>.</sub></p>", "minValue": "1464", "maxValue": "1465", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate product moment correlation coefficient r to 3 decimal places.</p>", "minValue": "0.975", "maxValue": "0.985", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Identify the equation of regression line of ice-cream sales on temperature</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["<p>Ice-cream sales = 2.801 x temperature &ndash; 164.44</p>\n<p></p>", "<p>Ice-cream sales = 2.85 x temperature &ndash; 164.64</p>\n<p>&nbsp;</p>", "<p>Ice-cream sales = 2.941 x temperature &ndash; 165.58</p>\n<p>&nbsp;</p>", "<p>Ice-cream sales = 2.7801 x temperature &ndash; 166.44</p>\n<p>&nbsp;</p>"], "matrix": ["4", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Predict the ice-cream sales (in weight) when the temperature in the city reaches&nbsp;102 <sup>o</sup> to 3 decimal places.</p>", "minValue": "121.255", "maxValue": "121.265", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}]}, {"name": "Chi-Square Hypothesis Test", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Shihan Miah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4456/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A research team is investigating the link between physical fitness level and suffering from severe headaches. 2400 people took part in the study. Their physical fitness level was measured. Each person was asked whether or not they suffered regularly from severe headaches.</p>\n<p>Table: study results</p>\n<table>\n<tbody>\n<tr style=\"height: 60px;\">\n<td style=\"width: 121.364px; height: 60px;\">\n<p><strong>&nbsp;</strong></p>\n</td>\n<td style=\"width: 142.273px; height: 60px;\">\n<p>Low fitness level</p>\n</td>\n<td style=\"width: 142.273px; height: 60px;\">\n<p>Moderate fitness level</p>\n</td>\n<td style=\"width: 145px; height: 60px;\">\n<p>High fitness level</p>\n</td>\n</tr>\n<tr style=\"height: 60px;\">\n<td style=\"width: 121.364px; height: 60px;\">\n<p>severe headaches</p>\n</td>\n<td style=\"width: 142.273px; height: 60px;\">\n<p>60</p>\n</td>\n<td style=\"width: 142.273px; height: 60px;\">\n<p>110</p>\n</td>\n<td style=\"width: 145px; height: 60px;\">\n<p>30</p>\n</td>\n</tr>\n<tr style=\"height: 60px;\">\n<td style=\"width: 121.364px; height: 60px;\">\n<p>no severe headaches</p>\n</td>\n<td style=\"width: 142.273px; height: 60px;\">\n<p>322</p>\n</td>\n<td style=\"width: 142.273px; height: 60px;\">\n<p>1250</p>\n</td>\n<td style=\"width: 145px; height: 60px;\">\n<p>620</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p>&nbsp;&nbsp;Use a suitable test at a 5% significance level to check if there is an association between fitness level and suffering from headaches.</p>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Which test is suitable for this problem?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["Proportion test", "t test", "Chi-Square test"], "matrix": [0, 0, "1"], "distractors": ["", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the null hypothesis?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["There is no association between physical fitness level and suffering from severe headaches", "<p>There is an association between physical fitness level and severe headaches.</p>"], "matrix": ["1", 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the alternative hypothesis?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["<p>There is an no association between physical fitness level and severe headaches.</p>", "<p>There is an association between physical fitness level and severe headaches.</p>", "None"], "matrix": [0, "1", 0], "distractors": ["", "", ""]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Write the number of degrees of freedom.</p>", "minValue": "2", "maxValue": "2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Write down the value of critical value to 2 decimal places.&nbsp;</p>", "minValue": "5.99", "maxValue": "5.995", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "7", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Write down the value of chi-square test statistics to 2 decimal places.</p>", "minValue": "38.8", "maxValue": "39.8", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the conclusion in this case?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["There is no evidence to reject null hypothesis", "There is enough evidence to reject null hypothesis"], "matrix": [0, "2"], "distractors": ["", ""]}]}, {"name": "Two Sample Hypothesis Test", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Shihan Miah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4456/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>A survey of passengers travelling from airports in London showed that passengers disliked waiting at security control. Two airports in London decide to investigate the issue.</p>\n<p>Heathrow Airport asked a random sample of 16 passengers to record how long they waited at security control. The mean waiting time for the sample was 31 minutes with a standard deviation of 7 minutes.</p>\n<p>London City Airport asked a random sample of 10 passengers to record the same information. The mean waiting time for the sample was 26 minutes with a standard deviation of 8 minutes.</p>\n<p>Assume that the waiting times for all passengers are normally distributed. Use a two sample t-test with a 5% significance level to determine if there is a &nbsp;&nbsp;&nbsp;difference in waiting times at Heathrow Airport and London City Airport.&nbsp;</p>", "advice": "<p>Fill the by writing appripriate words</p>", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>The null hypothesis is</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["<p>There is no difference between the wait times at Heathrow and City airports</p>", "<p>There is difference between the wait times at Heathrow and City airports</p>"], "matrix": ["1", 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>The alternative hypothesis is:&nbsp;</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": "1", "showCellAnswerState": false, "choices": ["<p>There is no difference between the wait times at Heathrow and City airports</p>", "<p>There is&nbsp; difference between the wait times at Heathrow and City airports</p>", "Wait time at Heatrow airport is more that at City airport"], "matrix": [0, "1", 0], "distractors": ["", "", ""]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Write down the number of degrees of freedom</p>", "minValue": "24", "maxValue": "24", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Write down the critical value to 2 decimal places at 5% significane level.</p>", "minValue": "2.063", "maxValue": "2.065", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "4", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate the pooled sample standard deviation Sp to 2 decimal places.</p>", "minValue": "7.38", "maxValue": "7.40", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "4", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate the test statistics to 2 decimal places.</p>", "minValue": "1.67", "maxValue": "1.69", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the conclusion?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["There is evidence to reject null hypothesis", "There is not enough evidence to reject null hypothesis"], "matrix": [0, "2"], "distractors": ["", ""]}]}, {"name": "Economic Order quantity", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Shihan Miah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4456/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A health food retailer sells cartons of protein shake powder which it purchases from a supplier. The demand for the protein shake powder is 6200 cartons per year. It costs the health food retailer &pound;50 per order to place an order with their supplier. Annual storage cost per carton is &pound;2.50</p>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate the EOQ for the purchase of the protein shake cartons.</p>", "minValue": "497", "maxValue": "499", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>The supplier offers a discount for larger orders. Use the supplier price list (shown below) to determine if it is better for the health food company to use a larger order quantity and get a discount on the price.&nbsp;</p>\n<p>Table : Supplier price schedule</p>\n<table>\n<tbody>\n<tr>\n<td width=\"163\">\n<p>Order Quantity</p>\n</td>\n<td width=\"167\">\n<p>Unit Price</p>\n</td>\n</tr>\n<tr>\n<td width=\"163\">\n<p>0 &ndash; 999</p>\n</td>\n<td width=\"167\">\n<p>&pound;3.60</p>\n</td>\n</tr>\n<tr>\n<td width=\"163\">\n<p>1000 or more</p>\n</td>\n<td width=\"167\">\n<p>&pound;3.00</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Calculate the total cost to the health food retailer at EOQ.&nbsp;</p>", "minValue": "23564", "maxValue": "23565", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate the total cost to the health food retailer at 1000 .</p>", "minValue": "20159", "maxValue": "20161", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "6", "showCorrectAnswer": false, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>The health food shop has determined that demand for cartons of protein shake powder is normally distributed with a mean of 20 per day and a standard deviation of 5.3. The lead time for receiving new stock is 5 days.</p>\n<p>Calculate the buffer stock level that the health food shop should hold if they want to ensure that there is a less than 5% chance of running out of stock.</p>", "minValue": "19", "maxValue": "21", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}]}]}], "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": false, "showtotalmark": false, "showanswerstate": false, "allowrevealanswer": false, "advicethreshold": 0, "intro": "", "feedbackmessages": []}, "contributors": [{"name": "Shihan Miah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4456/"}], "extensions": [], "custom_part_types": [], "resources": []}