I need help with these four questions and explain how arrived at each answer

1) You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.

A random sample of 35 gas grills has a mean price of $637.60. Assume the population standard deviation is $57.10.

The 90% confidence interval is ( , )

(Round to one decimal place as needed.)

The 95% confidence interval is ( , )

(Round to one decimal place as needed.)

2) A publisher wants to estimate the mean length of time (in minutes) all adults spend reading newspapers. To determine this estimate, the publisher takes a random sample of 15 people and obtains the results below. From past studies, the publisher assumes sigma is 2.1 minutes and that the population of times is normally distributed.

10

9

7

9

8

10

12

8

6

11

6

8

12

12

12

Construct the 90% and 99% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.

The 90% confidence interval is ( , )

(Round to one decimal place as needed.)

The 99% confidence intervals is ( , )

(Round to one decimal place as needed)

3) Construct the indicated confidence interval for the population mean mu using the t-distribution.

c equals=0.99, x over bar x equals=12.8, s equals=4.0, n equals=10

The 99% confidence interval using a t-distribution is left parenthesis nothing comma nothing right parenthesis .

,

.

(Round to one decimal place as needed.)

4)In a random sample of 26 people, the mean commute time to work was 32.5 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a t-distribution to construct a 98% confidence interval for the population mean mu . What is the margin of error of mu ? Interpret the results.

The confidence interval for the population mean mu is left parenthesis nothing comma nothing right parenthesis .

,

.

(Round to one decimal place as needed.)