If μ= 39.44 and σ=3, what is the critical value for the 95% interval when x̄=40 with sample size n=182?

Suppose we have two normal populations denoted A and B, and we want to compare their population variances by estimating the ratio: variance of population B divided by variance of population A.  We have an independent random sample of size 15 from population A and an independent random sample of size 9 from population B.  The sample variance for population B turns out to be 30 percent larger than that for population A.  What is the 99 percent confidence interval for the ratio:  population variance of population B divided by population variance of population A?  Use stattrek.org for finding the needed critical values.

In the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?

the 2nd part please

Consider the scenario ai from the previous question. Suppose you take an SRS of 50 avocados and find that the mean is 1.1 inches, which yields a p-value of 0.0542. What conclusion would you draw at the =0.05 level? At the =0.10level?

If a sample of n = 25 scores is selected from a normal population with µ = 100 and σ = 20, then the sample mean is expected to be around M = 100. Find the exact range of values that will contain the sample mean 80% of the time.