Please answer the following questions showing manual working out:

In an application to estimate the mean number of miles that downtown employees community to work roundtrip each day, the following information is given:

n=15

xbar = 7.82

s=2.00

Based on this information, the lower limit for a 90% confidence interval estimate for the true population is?

(Round answer to two decimal places. If your answer is 12.34%, write only 12.34, but do not write 0.1234)

A manager wishes to estimate a population mean using a 95% confidence interval estimate that has a margin of error of 15. If the population standard deviation is thought to be 154, what is the required sample size to the nearest whole number? Round the answer to the nearest whole number.

In a two-tailed hypothesis test for a population mean, a decrease in the sample size will:

a )have no effect on whether the null hypothesis is true or false.

b) have no effect on the significance level for the test.

c) result in a sampling distribution that has more variability.

d) All of the above are true.