A random sample of students at a college reported what they believed to be their heights in inches. Then the students measured each others' heights in centimeters, without shoes. The data provided are for the men, with their believed heights converted from inches to centimeters. Assume that conditions for t-tests hold. Complete parts a and b below. Click the icon to view the data. Data Table a. Find a 95% confidence interval for the mean difference as measured in centimeters. Does it capture 0? What does that show? The 95% confidence interval for measured - believed is() (Round to three decimal places as needed.) Men The interval include 0, so a hypothesis that the means are equal be rejected. Centimeters Centimeters (measured) (believed) 168 167.64 179 Full Data Set Centimeters Centimeters (measured) (believed) 177.80 172 170.18 175 177.80 b. Perform a t-test to test the hypothesis that the means are not the same. Use a significance level of 0.05. 186 187.96 180 177.80 Determine the hypotheses for this test. Let difference be the population mean difference between measured and believed height, in centimeters. Cho 167 170.18 175 177.80 189 193.04 171 167.64 173 170.18 171 167.64 OA. Ho Hdifference *0 Ha: Pdifference =0 OC. Ho Hdifference *0 Hai Hdifference >0 OE. Ho Hdifference =0 Ha: Haifference <0 Find the test statistic for measured - believed for this test. B. Ho-Hofference H- Hdifference OD. Ho Hdifference =0 =0 175 175.26 182 185.42 > 0 192 195.58 Ha difference #0 OF. Ho difference #0 Ha- Hdifference <0 Print Done t= (Round to two decimal places as needed.) Find the p-value for this test. p-value = (Round to three decimal places as needed.)