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Hypothesis Testing � Comparing Two Groups

Examines hypothesis testing methods for comparing two groups.

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    1 Hypothesis Testing – Comparing Two Groups 1 For each of the following research questions does the situation or research question involve independent samples or paired data? a. Do liberal arts majors and science majors have different 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 the house? Here the research question involves independent samples. d. Do families with at least one unemployed adult average more time watching TV per week than families in which all adults are employed? Here the research question involves independent samples . 2 In the Datasets folder open the GSS Dataset . The data are from the 2006 General Social Survey, a federally funded national survey done every other year by the University of Chicago. The variable marital indicates whether the respondent is presently married or not. We’ll compare the mean age ( Age is 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 for married people versus unmarried people). Here we want to test whether there is a significant difference between the population mean age between married and unmarried people or not. Thus the null hypothesis is there is no difference and 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. 𝐻 0 : μ ௨𝑛௠𝑎௥௥௜௘𝑑 − μ ௠𝑎௥௥௜௘𝑑 = 0 𝑎𝑛𝑑 𝐻 𝑎 : μ ௨𝑛௠𝑎௥௥௜௘𝑑 − μ ௠𝑎௥௥௜௘𝑑 ≠ 0 c. Recall from the lecture notes that when doing a two - sample t - test one consideration is whether the two standard deviations (or variances) are equal. To check, use software to find the standard deviation for Age for the two categories of marital status. In Minitab Express, you can get these SD by clicking Statistics > Descriptive Statistics and selecting Age for Variables and marital for Group variable. i. What are the two standard deviations? Std.dev for married: 15.051

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