// Numbas version: finer_feedback_settings
{"name": "Testing an hypothesis about the mean of a group (1).", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"pstdev": {"definition": "sqrt(abs(l)/(abs(l)-1))*stdev(l)", "type": "number", "parameters": [["l", "list"]], "language": "jme"}}, "ungrouped_variables": ["mu1", "r1", "sig1", "t95", "thismany", "tcalc", "tupper", "tlower", "mdupper", "mdlower", "stdupper", "stdlower", "outcome", "sed", "meanwgt", "sdwgt", "hypval"], "name": "Testing an hypothesis about the mean of a group (1).", "tags": ["average", "data analysis", "differences", "elementary statistics", "hypothesis testing", "mean", "mean of differences", "paired t-test", "standard deviation", "standard deviation of differences", "statistics", "stats", "t-test", "variance"], "advice": "<p>First, recognise that this is a&nbsp;one-sample (or \"mean to hypothetical value\") t-test.</p>\n<p>So calculate the mean&nbsp;of the sample:</p>\n<p style=\"padding-left: 30px;\">{meanwgt}</p>\n<p>Then the standard deviation (sd) of the sample:</p>\n<p style=\"padding-left: 30px;\">{sdwgt}</p>\n<p><strong>Note:</strong> You should use your calculator to get both the mean and standard deviation.</p>\n<p>The standard error (se) is calculated as:</p>\n<p>\\[ se = \\frac{ sd }{ \\sqrt{ n }} \\]</p>\n<p>It is:</p>\n<p style=\"padding-left: 30px;\">{sed}</p>\n<p>Finally, calculate the test statisitic, t-calc, as the mean difference divided by the standard error:</p>\n<p><span>\\[ t-calc&nbsp;= \\frac{ mean difference&nbsp;}{ se} \\]</span></p>\n<p style=\"padding-left: 30px;\"><span>t-calc = {tcalc}</span></p>\n<p><span>There are 6 {objects}, so 5 degrees of freedom, and the test is two-tailed, so the t-table = 2.571.</span></p>\n<p><span>If t-calc is greater than 2.571, the null is rejected. As this is a two-tailed test, the sign of t-calc (positive or negative) is ignored.</span></p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "<p>Find the mean and standard deviation of the&nbsp;sample.</p>\n<p>Mean &nbsp;= [[0]] (input&nbsp; to 2 decimal places&nbsp;)</p>\n<p>Standard deviation &nbsp;= [[1]] (input to 2 decimal places)</p>\n<p>Now find the one sample (or \"mean to hypothetical value\")&nbsp;t-test statistic using the values you have just calculated =[[2]] (input 2 decimal places)</p>\n<p>Is the null hypothesis rejected?&nbsp;[[3]] Enter 0 for \"No\" and 1 for \"Yes\".</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "2", "maxValue": "{mdupper}", "minValue": "{mdlower}", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "2", "maxValue": "{stdupper}", "minValue": "{stdlower}", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "2", "maxValue": "{tupper}", "minValue": "{tlower}", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "scripts": {}, "maxValue": "{outcome}", "minValue": "{outcome}", "correctAnswerFraction": false, "showCorrectAnswer": true, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "statement": "<p>The Arnott&rsquo;s biscuit company makes \"snack packs\" of many of its products, including Tiny Teddy (TT) and Pizza Shapes (PS). These packs are labelled \"25 g\". Test if TT&nbsp;meet the stated weight content. Sample data are in the table below:</p>\n<table>\n<tbody>\n<tr>\n<td><strong>{object}</strong></td>\n<td style=\"text-align: center;\"><strong>A</strong></td>\n<td style=\"text-align: center;\"><strong>B</strong></td>\n<td style=\"text-align: center;\"><strong>C</strong></td>\n<td style=\"text-align: center;\"><strong>D</strong></td>\n<td style=\"text-align: center;\"><strong>E</strong></td>\n<td style=\"text-align: center;\"><strong>F</strong></td>\n</tr>\n<tr>\n<td><strong>Weight (g)</strong></td>\n<td style=\"text-align: center;\"><span>$\\var{r1[0]}$</span></td>\n<td style=\"text-align: center;\"><span>$\\var{r1[1]}$</span></td>\n<td style=\"text-align: center;\"><span>$\\var{r1[2]}$</span></td>\n<td style=\"text-align: center;\"><span>$\\var{r1[3]}$</span></td>\n<td style=\"text-align: center;\"><span>$\\var{r1[4]}$</span></td>\n<td style=\"text-align: center;\"><span>$\\var{r1[5]}$</span></td>\n</tr>\n</tbody>\n</table>\n<p><strong>Are the packets, on average, the correct weight?</strong></p>\n<p>In other words, test the following null hypothesis:</p>\n<p style=\"padding-left: 30px;\">H0: Mean weight is equal to 25 g.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"mu1": {"definition": "random(22..28#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "mu1", "description": ""}, "r1": {"definition": "repeat(min(round(normalsample(mu1,sig1)),25),6)", "templateType": "anything", "group": "Ungrouped variables", "name": "r1", "description": ""}, "mdupper": {"definition": "meanwgt+0.025", "templateType": "anything", "group": "Ungrouped variables", "name": "mdupper", "description": ""}, "stdupper": {"definition": "sdwgt+0.025", "templateType": "anything", "group": "Ungrouped variables", "name": "stdupper", "description": ""}, "meanwgt": {"definition": "precround(mean(r1),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "meanwgt", "description": ""}, "hypval": {"definition": "25", "templateType": "anything", "group": "Ungrouped variables", "name": "hypval", "description": ""}, "sig1": {"definition": "random(2..3#0.2)", "templateType": "anything", "group": "Ungrouped variables", "name": "sig1", "description": ""}, "thismany": {"definition": "6", "templateType": "anything", "group": "Ungrouped variables", "name": "thismany", "description": ""}, "sed": {"definition": "precround(sdwgt/sqrt(thismany),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "sed", "description": ""}, "mdlower": {"definition": "meanwgt-0.025", "templateType": "anything", "group": "Ungrouped variables", "name": "mdlower", "description": ""}, "tupper": {"definition": "tcalc+0.025", "templateType": "anything", "group": "Ungrouped variables", "name": "tupper", "description": ""}, "tcalc": {"definition": "precround((meanwgt-hypval)/(sdwgt/sqrt(thismany)),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "tcalc", "description": ""}, "t95": {"definition": "2.571", "templateType": "anything", "group": "Ungrouped variables", "name": "t95", "description": ""}, "stdlower": {"definition": "sdwgt-0.025", "templateType": "anything", "group": "Ungrouped variables", "name": "stdlower", "description": ""}, "outcome": {"definition": "if((abs(tcalc)>t95),1,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "outcome", "description": ""}, "sdwgt": {"definition": "precround(pstdev(r1),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "sdwgt", "description": ""}, "tlower": {"definition": "tcalc-0.025", "templateType": "anything", "group": "Ungrouped variables", "name": "tlower", "description": ""}}, "metadata": {"notes": "", "description": "<p>Testing an hypothesis about the mean of one group.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Keith McGuinness", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/523/"}]}]}], "contributors": [{"name": "Keith McGuinness", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/523/"}]}