You have reason to believe that senior managers spend more time working outside the office, on average, than middle managers. To investigate this suspicion, you gather random samples from both groups. You take a sample of 15 senior managers and find a sample mean 51.2 minutes per day; for the sample of 20 middle managers, the mean was 47.1 minutes per day. Assume that you know the standard deviation (not variance) for each population (16 for senior,15 for middle).

1.) Determine the point estimate for the difference between population means

2.) The next several questions refer to determing a confidence interval for the difference in population means, at the 95% confidence level. a.)What is the z or t score to be used (to at least three decimals)?

b.) What is the margin of error (E) (to at least three decimals)?

c.) What is the LOWER limit of the interval (to at least three decimals)?

3.) The next several questions refer to doing a hypothesis test that the population mean for population 1 is greater than that for population 2, at a 99% confidence level.

a.) What is the correct alternative hypothesis?

b.) What is D0?

c.) What is the value of the test statistic (i.e., z, t, chi-square, F, etc.--depending on the test/distribution you are using)? Give your answer to at least three decimal places.

d.) What formula should be used to calculate the p-value, if doing the calculation without a tool? (Here concentrate the on the structure. CDF refers to whichever distribution you are using: norm.s.dist, t.dist, etc.)

e.) What is the p-value (to at least three decimal places)?

f.) What is the correct conclusion?