// Numbas version: exam_results_page_options
{"name": "Final Exam 2019-2020", "metadata": {"description": "", "licence": "None specified"}, "duration": 7200, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"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": "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": ["", "", "", ""]}]}]}], "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": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "feedbackmessages": []}, "contributors": [{"name": "Shihan Miah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4456/"}], "extensions": [], "custom_part_types": [], "resources": []}