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 wights (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 95% confidence interval for the average weight of the metal rings made by Whitcomb Company.
(b) Test at 5% 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)
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