Self-Reported Heights of Men (Example 12) A random sample of students reported what they believed to be their height in inches, which were then converted to centimetres. Then the students measured each other's heights in centimetres, without shoes. The data shown are for the men. Assume that the conditions the test hold. a. Find a 95% confidence interval for the mean difference in the reported height and the actual height. Does it capture 0? What does that show? b. Perform a statistical test to test the hypothesis that the means are not the same. Use a significance level of 0.05, and show all four steps. Height (cm) (reported in inches and converted to cm) 167.64 172.72 185.42 Height (cm) Measured 168 172 184 170.18 168 193.04 191 173 172.72 175.26 174 193.04 191 177.8 178 175.26 177 180.34 181 175.26 175 170.18 171 170.18 170