Ten individuals went o t for 12 weeks to lower thei test at the 5% level. starting cholesterol level Ending cholesterol level 220 220 -200 280 260 240 NOTE: If you are using a Student's t-distribution for the problem, including for paired data, outed. (In general, you must first prove that assumption, though.) ( Part ( 2 ) State the null hypothesis. O HO: Ma = 0 O HO : 1 0 = 0 O HO : My = 0 O HO : H g 20 Part (b ) State the alternative hypothesis . O Ha: My20 O Ha Ha > 0 Part ( c) words, state what your random variable Xy represents. O Xy represents the average difference in the cholesterol level before and after the diet. O Xy represents the total difference in cholesterol levels before and after the diet. O Xy represents the average cholesterol level of the 10 individuals. O Xy represents the difference in the average cholesterol level before and after the diet. 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 ) -Select- = 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.) Part ( 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 g cholesterol levels is at most -8. vels is less than -8. O If Ho is false, then there is a chance equal to the p-valu holesterol levels is less than - 8. If Ho is false, then sterol levels is at most -8. Part ( 9 ) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. - Ka p-value - Ka 1/2(p-value 1/2(p-value: 1/2(p-value 1/2 (p-value; . Xa - Ka Part (h Indicate the correct decision ('reject or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (1) Alpha (Enter an exact number as an integer, fraction, or decimal.) a = (i) Decision: "O reject the null hypothesis O do not reject the null hypothesis i) Reason for decision: Since p-value > c, we reject the null hypothesis. O Since p-value