Question

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 sigmaσ 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 muμ 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 μ. What is the margin of error of mu μ​? Interpret the results.

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

,

.

​(Round to one decimal place as​ needed.)

 

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