'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 150 150 200 210 110 130 240 220 200 190 180 150 190 200 360 300 280 300 260 240 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.) State the distribution to use for the test. (Enter your answer in the form 2 or tdfwhere df is the degrees of freedom) X El Part (e) What is the test statistic? (If using the 1 distribution round your answer to two decimal places, and if using the tdistribution round your answer to three decimal places.) ' 9= x B Par! (0 What is the pvalue? (Round your answer to four decimal places.) X Explain what the pvalue means for this problem. '\\ lf H0 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 -8. lf H0 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 -8. ' i If H0 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 -8. o If H0 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 -8. Incorrect. A pvalue is the probability that an outcome at least as extreme as the sample data will happen purely by chance when H0 is true. 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.) a = X (ii) Decision: reject the null hypothesis 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. Since p-value