Problem 1: Sleep deprivation • a class survey, students were asked how many hours they sleep per night. Data of based on 19 students' feedback is given below: • 344455556 • 77888999 a. Construct a boxplot of the data b. Can we assume that the data is selected from a normal distribution? c. Calculate a two-sided 95% confidence interval for the true average of sleep time • Find the sample standard deviation s=E(xi-)2ni=1n-1 • Since u (population mean) and o (population standard deviation) are unknow, we will use the T statistic T=x-pµS/n • T- ta 2,n-1 • Confidence interval Cl=(X-ta 2,n-1.svn,X+ta 2,n-1.svn) Problem 2 a. Given a pair of p-values and significance levels a, state whether the observed p%3Dvalue would lead to rejection of H0 at the given significance level. • p= 0.092, a=0.05 • p =0.001, a=0.05 b. Determine the t critical value for a two-sided confidence interval • Confidence level = 98%, df = 8 t = • Confidence level = 95%, df = 36 t =