1. A machine produces 3-inch nails. A sample of 10 nails was selected and the le

1. A machine produces 3-inch nails. A sample of 10 nails was selected and the lengths determined. the results are follows: 2.89 2.95 3.00 3.05 2.99 2.96 3.10 3.06 3.00 3.12. Use these results to test Ho: m= 3 ans Ha: m not equal 3 at alpha = 0.01. Give the critical region the computed test statistic and the conclusion. 2. A machine produces 3-inch nails. A sample of 100 nails is selected and it is found that 25 are shorter than 3 inches. Find the 95% confidence interval on the proportion of all such nails that are shorter than 3 inches. 3. A sample of size n = 14 is selected from a normal population to construct a 95% confidence interval estimate for a popultion mean. The interval was computed to be (7.82 to 9.64). Determine the sample standard deviation. 4. Determine the p-value for each of the following hypothesis -testing situations: a. Ho_p= 0.25 and Ha:p not equal 0.25; test value = 1.84. b. Ho_m=>or equal to 13.5 and Ha:m