(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 Husband's score 3 2 2 1 2 2 3 3 4 2 1 1 2 4 2 1 1 1 2 4 NOTE: If you are using a Student's t-distribution 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.) Part (a) State the null hypothesis. ○ Ho: μd>0 ○ Ho: Md #0 ○ Ho Hd <0 ○ Ho Hd20 Part (b) State the alternative hypothesis. ○ Hai Hd <0 ○ Hai Hd>0 ○ Hai Hd #0 Part (c) In words, state what your random variable X represents. OX represents the difference in the average satisfaction level of husbands and wives. ○ X represents the average satisfaction level of husbands and wives. ○ X represents the difference in the satisfaction levels of husbands and wives. OX represents the average difference in the husbands' and the wives' satisfaction levels. Part (d) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.) Part (e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) --Select-- = Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If Ho is false, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is greater than -0.5. ○ If Ho is false, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is at most -0.5. If Ho is true, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is greater than -0.5. ○ If Ho is true, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is at most -0.5. Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. Ал 1/2(p-value) 1/2(p-value) p-value Xd Χα 1/2(p-value) 1/2(p-value) p-value Χα Χα Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) απ (ii) Decision: O reject the null hypothesis O do not reject the null hypothesis (iii) Reason for decision: ○ Since p-value>a, we do not reject the null hypothesis. Since p-value a, we reject the null hypothesis. O Since p-value