98_5 87.0 75.7 87.3 106.5 x-90.08 83.6 86.7 82.3 106.6 86.6 Sample statistics: 4. The dataset above is a random sample from a Normal population with unknown mean g and unknown variance (a) Is there sufficient evidence to conclude that the mean Of the population, g, is different than 100? Perform the test at the 5% significance level. (Hint: this is a two-sided I-test) (b) Approximate the p-value Of the test using the available values in the I-table. (c) What is the conclusion at the 1% level? (d) Construct a 95% confidence interval for the mean Of the population. (e) Construct a 99% confidence interval for the mean of the population. (f) Would a 900/0 confidence interval be narrower or wider than the 95% confidence interval? 5. Is there sufflcient evidence to conclude that the population variance exceeds 100 (i.e., 52 > 100)? Perform the appropriate test at the 5% significance level. 6. Construct a 95% lower confidence limit for the population variance, Is the hypothesized population variance Of 100 from the previous problem in the resulting interval?