Please help me with all parts for this question. Thank you so much!

part e options: z, t

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). Wife's score 2 2 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 tdistribution 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] Part (a) State the null hypothesis. 0 H0: [4,, 0 OHO:,4,,0 - Part (b) State the alternative hypothesis. 0 Ha: [4,, > o OHa:;4d=0 OHa:;4d a, we reject the null hypothesis. 0 Since p-value 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. - Part (i) Explain how you determined which distribution to use. 0 The t-distribution will be used because the samples are dependent. O The t-distribution 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 difference in proportions. O The standard normal distribution will be used because the samples are independent and the population standard deviation is known. .lL