Problem 1. (2 points) The Whitcomb Company manufactures a metal ring for industrial engines that usually weighs about 50 ounces. A random sample of 50 of these metal rings produced the following weights (in ounces).

51 53 56 50 44 47

53 53 42 57 46 55

41 44 52 56 50 57

44 46 41 52 69 53

57 51 54 63 42 47

47 52 53 46 36 58

51 38 49 50 62 39

44 55 43 52 43 42

57 49

(a) Construct a 99% confidence interval for the average weight of the metal rings made by Whitcomb company. (b) Test at 1% significance level to determine if the metal rings made by Whitcomb Company have an average weight less than 50 ounces. (Hint: you have to first calculate the sample size, sample mean, and sample standard deviation; and then apply the appropriate statistical inference techniques)