1. [9/14 Points] DETAILS PREVIOUS ANSWERS ILLOWSKYINTROSTAT1 10.1.080.HW. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER At Rachel's 11th birthday party, 8 girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis at the 5% level. Relaxed time (seconds) Jumping time (seconds) 26 21 45 42 28 26 22 21 23 25 45 43 37 35 29 32 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) +) Part (b) (+) Part (c) - Part (d) State the distribution to use for the test. (Enter your answer in the form z or tay 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--- v = Part (f) What is the p-value? (Round your answer to four decimal places.)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 3 4 2 3 4 2 2 4 Husband's score 2 1 3 2 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) + Part (b) + Part (c) Part (d) State the distribution to use for the test. (Enter your answer in the form z or toy where of 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--- v = 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 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 -0.8. 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 -0.8. O 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 -0.8. 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 -0.8 Correct! A p-value is the probability that an outcome of the data will happen purely by chance when Ho is true.In the American society, birthdays are one of those days that everyone looks forward to. People of different ages and peer groups gather to mark the 18", 20", . . ., birthdays. During this time, one looks back to see what he or she has achieved for the past year and also focuses ahead for more to come. If, by any chance, I am invited to one of these parties, my experience is always different. Instead of dancing around with my friends while the music is booming, I get carried away by memories of my family back home in Kenya. I remember the good times I had with my brothers and sister while we did our daily routine. Every morning, I remember we went to the shamba (garden) to weed our crops. I remember one day arguing with my brother as to why he always remained behind just to join us an hour later. In his defense, he said that he preferred waiting for breakfast before he came to weed. He said, "This is why I always work more hours than you guys!" And so, to prove him wrong or right, we decided to give it a try. One day we went to work as usual without breakfast, and recorded the time we could work before getting tired and stopping. On the next day, we all ate breakfast before going to work. We recorded how long we worked again before getting tired and stopping. Of interest was our mean increase in work time. Though not sure, my brother insisted that it was more than two hours. Using the data in the table below, solve our problem. (Use a = 0.05) Work hours with breakfast Work hours without breakfast 8 6 7 C UT 9 5 4 9 7 8 7 10 7 6 9 5 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) + Part (b) + Part (c) Part (d) State the distribution to use for the test. (Enter your answer in the form z or taywhere 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--- v = Part (f) What is the p-value? (Round your answer to four decimal places.)4. [10/14 Points] DETAILS PREVIOUS ANSWERS ILLOWSKYINTROSTAT1 10.4.115.HW. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Ten individuals went on a low-fat diet for 12 weeks to lower their cholesterol. The data are recorded in the table below. Do you think that their cholesterol levels were significantly lowered? Conduct a hypothesis test at the 5% level. Starting cholesterol level Ending cholesterol level 140 140 220 240 110 130 240 220 200 190 180 150 190 200 360 300 280 300 260 240 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) + Part (b) + Part (c) Part (d) State the distribution to use for the test. (Enter your answer in the form z or toywhere 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. O If Ho is true, then there is a chance equal to the p-value that the sample average difference between ending and starting cholesterol levels is less than -7. If Ho is false, then there is a chance equal to the p-value that the sample average difference between ending and starting cholesterol levels is less than -7. If Ho is true, then there is a chance equal to the p-value that the sample average difference between ending and starting cholesterol levels is at most -7. If Ho is false, then there is a chance equal to the p-value that the sample average difference between ending and starting cholesterol levels is at most -7