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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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