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 150 150 220 230 110 130 240 220 200 190 180 150 190 200 360 300 280 300 260 240 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 to 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--- = Part (f) What is the p-value? (Round your answer to four decimal places.)A traveler wanted to know if the prices of hotels are different in the ten cities that he visits the most often. The list of the cities with the correspondin hotel prices for his two favorite hotel chains is in the table below. Test at the 1% level of significance. (Use Hilton prices - Hyatt prices for the difference.) Cities Hyatt Regency prices in dollars Hilton prices in dollars Atlanta 109 170 Boston 356 286 Chicago 208 298 Dallas 209 198 Denver 167 169 Indianapolis 179 214 Los Angeles 179 169 New York City 625 459 Philadelphia 179 159 Washington, DC 245 239 + Part (a) + Part (b) + Part (c) Part (d) State the distribution to use for the test. (Enter your answer in the form z or to 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.)