Q1

One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, \"I'm pleased with the way we divide the responsibilities for childcare." The ratings went from 1 (strongly agree) to 5 (strongly disagree). The table below contains ten of the paired responses for husbands and wives. Conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife). 5 score 3 4 2 3 4 2 1 1 2 4 Husband's score 2 1 1 3 2 1 1 1 2 4 NOTE: If you are using a Student's t-distribution for the pro alem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) El Pan (a) State the null hypotheSis O Ho ya x o 0 Ho' #91 o O Ho- pd 2 0 El Pan (b) State the alternative hypothesis. 0 Ha #d : O 0 Ha. pa # O 0 H; w 0 0 Ha pd a, we reject the null hypothesis. 0 Since pvalue > a, we do not reject the null hypothesis. (iv) Conclusion: 0 There is sufcient evidence to show that. on average. the husbands are more pleased than the wives with the division of childcare. 0 There is not sufcient evidence to show that, on average, the husbands are more pleased than the wives with the division of childcare. El Part [i] Explain hovir you determined which distribution to use. 0 "he standard normal distribution will be used because the samples are independent and the population standard deviation is known. 0 'he standard normal distribution will be used because the samples involve the difference in proportions. 0 "he tdistribution will be used because the samples are dependent. 0 'he tdistribution will be used because the samples are independent and the population standard deviation is not known. \fState the altemative hypothesis. 0 Ha: pa: 0 O Haqudat OHa:pd>t} OHazpazo OHa:pa 0.100 Explain what the p-value means for this problem. O If Ho is true, then there is a chance equal to the p-value that the difference in the sample mean of the prices at the Hyatt Regency and Hilton hotels is at most 9.6. O If Ho is false, then there is a chance equal to the p-value that the difference in the sample mean of the prices at the Hyatt Regency and Hilton hotels is at least 9.6. O If Ho is false, then there is a chance equal to the p-value that the difference in the sample mean of the prices at the Hyatt Regency and Hilton hotels is at most 9.6. O If Ho is true, then there is a chance equal to the p-value that the difference in the sample mean of the prices at the Hyatt Regency and Hilton hotels is at least 9.6.\fEl Part [II] Indicate the correct decision ("reject" or "do not reject" the null hypothesis}, the reason for it, and write an appropriate conclusion. (ijAlpha (Enter an exact number as an integer, fraction, or decimal.) (ii) Decision: 0 reject the null hypothesis 0 do not reject the null hypothesis (iii) Reason for decision: 0 Since pvalue a, we reject the null hypothesis. (iv) Conclusion: 0 There is sufcient evidenoe to show that the average post-course SAT score is larger than the average pre-course SAT score. 0 There is not sufcient evidence to show that the average postcourse SAT score is larger than the average precourse SAT score. B Paniii Explain how you determined which distribution to use. 0 The standard normal distribution will be used because the samples are independent and the population standard deviation is known. 0 The Mistribution Will be used because the samples are dependent. O The Mistribution Will be used because the samples are independent and the population standard deviation is not known. 0 The standard normal distribution will be used because the samples involve the ditTerence in proportions. A new SAT study course is tested on 12 individuals. Prescourse and postscourse scores are recorded. Of interest is the average increase in SAT scores. The following data ls collected. Conduct a hypothesis test at the 5% level. Dre-course score Post-course score 1230 1340 950 930 1030 1150 840 880 1100 1070 1250 1320 860 860 1330 1370 790 770 990 1040 1110 1200 740 850 NOTE: If you are usmg a Student's redistribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) E Parl(a) Slate the null hypothesis 0 Ho' #a> 0 O H0 #0.: o O HO p.04) 0 H0 110.50