[25) You are an engineer testing the thickness of eyeglasses for a supervisor. A sample of 10 lenses yields a mean thickness of 2.95 mm and standard deviation 0.34 mm. The engineer would like the true average thickness of such lenses to be less than 3 .20 mm. Assume that the underlying distribution is normal and using a type I error rate of 10%: (5 )'What distribution will you use for the critical point and why b. (5} W'onld you create a condence intervaL upper bound or lower bound? (Explain) c. (10) Find the condence interval or bound that you choose in part b and interpret it (1. (5} Give the realworld answer 5\" (25} Suppose we want to determine if a new drug was effective at causing weight loss. To determine this= we randomly select 10 su b_jects~ and weighed them before and after treatment. The resulting summary data for the differences is given below. Assume that the differences come from a normal distribution and the data below is based on before after. Sample Size Sample Differences Mean Sample Differences Standard Deviation 7.52 (5) Would you use a t or 2 test in this case? Explain (5) Give the null and alternative hypotheses (10) Run the test based on your choice in part a and make your decision (5) Draw conclusions based on the realworld question 9.5": 94