Hypothesis Testing � Comparing Two Groups

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1Hypothesis Testing–Comparing Two Groups1For each of the following research questions does the situation or research question involveindependent samples or paired data?a.Do liberal arts majors and science majors havedifferent SAT verbal scores, on average?Here the research question involves independent samples.b.Does a caffeine pill help Autistic patients score higher on a cognitive exam?Here the research question involves paired data.c.In heterosexual relationships, does the man or the woman average more time outside thehouse?Here the research question involves independent samples.d.Do families with at least one unemployed adult average more time watching TV per week thanfamilies in which all adults are employed?Here the research question involves independent samples.2In theDatasets folderopen theGSS Dataset.The data are from the 2006 General SocialSurvey, a federally funded national survey done every other year by the University of Chicago.The variablemaritalindicates whether the respondent is presently married or not. We’ll comparethemeanage (Ageis the variable) for those who are married versus those who are not.a.In words, write a null hypothesis for this situation. We’re comparing two means (age formarried people versus unmarried people).Here we want to test whether there is a significant difference between the population mean agebetween married and unmarried people or not. Thus the null hypothesis is there is no differenceand the alternative is that there is a significant difference between the two mean.b.Using statistical notation for means write null and alternative hypotheses for this problem.𝐻0:μ௨𝑛௠𝑎௥௥௜௘𝑑−μ௠𝑎௥௥௜௘𝑑=0𝑎𝑛𝑑𝐻𝑎:μ௨𝑛௠𝑎௥௥௜௘𝑑−μ௠𝑎௥௥௜௘𝑑≠0c.Recall from the lecture notes that when doing a two-sample t-test one consideration is whetherthe two standard deviations (or variances) are equal. To check, use software to find the standarddeviation forAgefor the two categories ofmaritalstatus. In Minitab Express, you can get theseSD by clicking Statistics > Descriptive Statistics and selecting Age for Variables and marital forGroup variable.i.What are the two standard deviations?Std.dev for married:15.051

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