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 47 people, the mean body mass index (BMI) was 26.2 and the standard deviation was 6.11. Which distribution should be used to construct the confidence interval? Choose the correct answer below. A. Use a normal distribution because the sample is random, the population is normal, and σ is known. B. Use a t-distribution because the sample is random, the population is normal, and σ is unknown. C. Use a t-distribution because the sample is random, n≥30, and σ is unknown. D. Use a normal distribution because the sample is random, n≥30, and σ is known. E. Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or n<30, and the population is not known to be normal. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. A. The 99% confidence interval is (enter your response here,enter your response here). (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 people have a BMI between the bounds of the confidence interval. B. With 99% confidence, it can be said that the population mean BMI is between the bounds of the confidence interval. C. If a large sample of people are taken approximately 99% of them will have a BMI between the bounds of the confidence interval. D. Neither distribution can be used to construct the confidence interval.

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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Related questions

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

people, the mean body mass index (BMI) was

26.2

and the standard deviation was

6.11.

Which distribution should be used to construct the confidence interval? Choose the correct answer below.

Use a normal distribution because the sample is random, the population is normal, and

is known.

Use a t-distribution because the sample is random, the population is normal, and

is unknown.

Use a t-distribution because the sample is random,

n≥30,

and

is unknown.

Use a normal distribution because the sample is random,

n≥30,

and

is known.

Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or

n<30,

and the population is not known to be normal.

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

The

99%

confidence interval is

(enter your response here,enter your response here).

(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 people have a BMI between the bounds of the confidence interval.

With

99%

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

If a large sample of people are taken approximately

99%

of them will have a BMI between the bounds of the confidence interval.

Neither distribution can be used to construct the confidence interval.

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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