An article in the San Jose Mercury News stated that students in the California state university...

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An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 47 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level? Note: If you are using a Student's t-distribution for the problem, 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: M 4.5 Ho: #4.5 : > 4.5 Ho: <4.5 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.) T 46 Part (e) What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.) t = 3.438 + Part (i) Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to two decimal places.) 95% C.I. 4.69 5.50 Additional Materials 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 corresponding 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 107 168 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 (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.) t = 0.434 > Part (f) What is the p-value? (Round your answer to four decimal places.) 0.6745 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 difference in the sample mean of the prices at the Hyatt Regency and Hilton hotels is at most 9.5. If Ho is true, then there is a chance equal to the p-value that the difference in the sample mean of the prices at the Hyatt Regency and Hilton hotels is at least 9.5. If Ho is false, then there is a chance equal to the p-value that the difference in the sample mean of the prices at the Hyatt Regency and Hilton hotels is at least 9.5. If Ho is true, then there is a chance equal to the p-value that the difference in the sample mean of the prices at the Hyatt Regency and Hilton hotels is at most 9.5. An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 47 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level? Note: If you are using a Student's t-distribution for the problem, 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: M 4.5 Ho: #4.5 : > 4.5 Ho: <4.5 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.) T 46 Part (e) What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.) t = 3.438 + Part (i) Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to two decimal places.) 95% C.I. 4.69 5.50 Additional Materials 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 corresponding 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 107 168 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 (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.) t = 0.434 > Part (f) What is the p-value? (Round your answer to four decimal places.) 0.6745 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 difference in the sample mean of the prices at the Hyatt Regency and Hilton hotels is at most 9.5. If Ho is true, then there is a chance equal to the p-value that the difference in the sample mean of the prices at the Hyatt Regency and Hilton hotels is at least 9.5. If Ho is false, then there is a chance equal to the p-value that the difference in the sample mean of the prices at the Hyatt Regency and Hilton hotels is at least 9.5. If Ho is true, then there is a chance equal to the p-value that the difference in the sample mean of the prices at the Hyatt Regency and Hilton hotels is at most 9.5.