Use the standard normal distribution or the t-distribution to construct a 99% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 11 mortgage institutions, the mean interest rate was 3.66% and the standard deviation was 0.32%. Assume the interest rates are normally distributed. Which distribution should be used to construct the confidence interval? A. Use a normal distribution because n<30 and the interest rates are normally distributed. B. Use a t-distribution because the interest rates are normally distributed and σ is known. C. Use a normal distribution because the interest rates are normally distributed and σ is known. D. Use a t-distribution because it is a random sample, σ is unknown, and the interest rates are normally distributed. E. Cannot use the standard normal distribution or the t-distribution because σ is unknown, n<30, and the interest rates are not normally distributed. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. A. The 99% confidence interval is (nothing,nothing). (Round to two decimal places as needed.) B. Neither distribution can be used to construct the confidence interval. Interpret the results. Choose the correct answer below. A. It can be said that 99% of institutions have an interest rate between the bounds of the confidence interval. B. If a large sample of institutions are taken approximately 99% of them will have an interest rate between the bounds of the confidence interval. C. With 99% confidence, it can be said that the population mean interest rate is between the bounds of the confidence interval. D. Neither distribution can be used to construct the confidence interval. Click to select your answer.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Use the standard normal distribution or the t-distribution to construct a

99%

confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results.

In a random sample of

mortgage institutions, the mean interest rate was

3.66%

and the standard deviation was

0.32%.

Assume the interest rates are normally distributed.

Which distribution should be used to construct the confidence interval?

Use a normal distribution because

n<30

and the interest rates are normally distributed.

Use a t-distribution because the interest rates are normally distributed and

is known.

Use a normal distribution because the interest rates are normally distributed and

is known.

Use a t-distribution because it is a random sample,

is unknown, and the interest rates are normally distributed.

Cannot use the standard normal distribution or the t-distribution because

is unknown,

n<30,

and the interest rates are not normally distributed.

Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.

The

99%

confidence interval is

(nothing,nothing).

(Round to two decimal places as needed.)

Neither distribution can be used to construct the confidence interval.

Interpret the results. Choose the correct answer below.

It can be said that

99%

of institutions have an interest rate between the bounds of the confidence interval.

If a large sample of institutions are taken approximately

99%

of them will have an interest rate between the bounds of the confidence interval.

With

99%

confidence, it can be said that the population mean interest rate is between the bounds of the confidence interval.

Neither distribution can be used to construct the confidence interval.

Click to select your answer.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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