// Numbas version: exam_results_page_options
{"name": "Two Sample Hypothesis Test ( class test)", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "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": "Two Sample Hypothesis Test ( Paired 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": "<ol>\n<li>The times taken for ten men to perform a task were measured. After training, designed to reduce the time, the men were tested again. The times in seconds were found and were as follows:</li>\n</ol>\n<p>&nbsp;</p>\n<table>\n<tbody>\n<tr>\n<td width=\"111\">\n<p>Man</p>\n</td>\n<td width=\"57\">\n<p>A</p>\n</td>\n<td width=\"57\">\n<p>B</p>\n</td>\n<td width=\"47\">\n<p>C</p>\n</td>\n<td width=\"47\">\n<p>D</p>\n</td>\n<td width=\"47\">\n<p>E</p>\n</td>\n<td width=\"47\">\n<p>F</p>\n</td>\n<td width=\"47\">\n<p>G</p>\n</td>\n<td width=\"47\">\n<p>H</p>\n</td>\n<td width=\"47\">\n<p>I</p>\n</td>\n<td width=\"42\">\n<p>J</p>\n</td>\n</tr>\n<tr>\n<td width=\"111\">\n<p>Time before</p>\n</td>\n<td width=\"57\">\n<p>27</p>\n</td>\n<td width=\"57\">\n<p>45</p>\n</td>\n<td width=\"47\">\n<p>51</p>\n</td>\n<td width=\"47\">\n<p>33</p>\n</td>\n<td width=\"47\">\n<p>49</p>\n</td>\n<td width=\"47\">\n<p>22</p>\n</td>\n<td width=\"47\">\n<p>23</p>\n</td>\n<td width=\"47\">\n<p>35</p>\n</td>\n<td width=\"47\">\n<p>41</p>\n</td>\n<td width=\"42\">\n<p>25</p>\n</td>\n</tr>\n<tr>\n<td width=\"111\">\n<p>Time after</p>\n</td>\n<td width=\"57\">\n<p>22</p>\n</td>\n<td width=\"57\">\n<p>37</p>\n</td>\n<td width=\"47\">\n<p>45</p>\n</td>\n<td width=\"47\">\n<p>26</p>\n</td>\n<td width=\"47\">\n<p>44</p>\n</td>\n<td width=\"47\">\n<p>20</p>\n</td>\n<td width=\"47\">\n<p>16</p>\n</td>\n<td width=\"47\">\n<p>35</p>\n</td>\n<td width=\"47\">\n<p>42</p>\n</td>\n<td width=\"42\">\n<p>23</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p>&nbsp;</p>\n<p>Report on the effectiveness of the training as shown by this experiment. <em>(Hint: this is a paired sample test, and as the sample is small we need to use a t test)</em></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": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Which one is the correct null hypothesis?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p><em>&nbsp;H<sub>0</sub>: there are no difference between the training time</em></p>", "<em>&nbsp;H<sub>0</sub>: there are difference between the training time</em>", "<em>&nbsp;H<sub>0</sub>:&nbsp; Training time is more before the training than after the training&nbsp;</em>", "<em>H<sub>0</sub>:&nbsp; Training time is less before the training than after the training&nbsp;</em>"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Which one is the correct alternative hypothesis?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<em>H<sub>1</sub>:&nbsp;&nbsp;there are no difference between training time</em>", "<em>H<sub>1</sub>:&nbsp; There are difference between the training time</em>", "<em>H<sub>1</sub>:&nbsp; Training time is more before the training than after the training&nbsp;</em>", "<em>H<sub>1</sub>:&nbsp; Training time is less before the training than after the training&nbsp;</em>"], "matrix": [0, 0, "1", 0], "distractors": ["", "", "", ""]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the critical&nbsp; value at 5% significance level (3d.p.)</p>", "minValue": "1.83", "maxValue": "1.84", "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": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate the test statistics ( 2d.p.)</p>", "minValue": "4.12", "maxValue": "4.14", "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": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Which one is the correct decesion?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["Reject null hypothesis", "Accept null hypothesis"], "matrix": ["2", 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the conclusion</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["Training is effective", "training is not effective"], "matrix": ["2", 0], "distractors": ["", ""]}]}, {"name": "Two Sample Hypothesis Test Revision", "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>The management in a large chain of shops aims to reduce the level of absenteeism among its staff. The management looks at two locations, a city centre shop in Manchester and a shop in Edinburgh.</p>\n<p>The company take a sample of 8 employee records in Manchester and record how many days each employee has been absent over the previous year. They find that the sample mean is 7 days with a sample standard deviation of 1.2</p>\n<p>They take a sample of 10 employees in Edinburgh and find that the sample mean is 6.2 with a sample standard deviation of 1.8. Carry out a two-sample t-test at a 5% significance level to determine if there is a difference in absenteeism between the two locations</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": true, "showFeedbackIcon": true, "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": true, "choices": ["<p>There is no difference between the stores.</p>", "<p>There is difference between the stores</p>"], "matrix": ["1", 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "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": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>There is no difference between the stores</p>", "<p>There is difference between the stores</p>"], "matrix": [0, "1"], "distractors": ["", ""]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate pooled sampled standard deviation to 2 decimal places.</p>", "minValue": "1.5", "maxValue": "1.6", "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": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate test statistics to 2 decimal places.</p>", "minValue": "1.0", "maxValue": "1.3", "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": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the number of degrees of freedom?</p>", "minValue": "16", "maxValue": "16", "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": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Write down the critical value.</p>", "minValue": "2.1", "maxValue": "2.2", "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": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the decision?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["There is not enough evidance to reject null hypothesis.", "There is enough evidance to reject null hypothesis."], "matrix": ["1", 0], "distractors": ["", ""]}]}]}], "navigation": 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