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Chapter 8: Q 17. (page 508)

Explaining confidence A 95%confidence interval for the mean body mass index (BMI) of young American women is 26.8卤0.6. Discuss whether each of the following explanations is correct, based on that information.

a. We are confident that 95%of all young women have BMI between 26.2and 27.4.

b. We are 95%confident that future samples of young women will have mean BMI

between 26.2and27.4.

c. Any value from 26.2to27.4is believable as the true mean BMI of young American women.

d. If we take many samples, the population mean BMI will be between 26.2and 27.4in about 95%of those samples.

e. The mean BMI of young American women cannot be 28.

Short Answer

Expert verified

a. Statement a is incorrect.

b. Statement b is incorrect.

c. Statement c is correct.

d. Statement d is incorrect.

e. Statement e is incorrect.

Step by step solution

01

Given Information

It is given that 95%confidence interval for mean body index is(26.2,27.4)

02

To Explain statement a is correct or not on the basis of given information.

From given data, it is incorrect because confidence interval is about BMI of young women, not about BMI of individual women.

03

To Explain statement b is correct or not on the basis of given information.

The statement is incorrect because it is not confirmed that true population mean is between 26.2and27.4.

The mean may or may not lie in confidence interval for further samples.

The statement is incorrect.

04

To Explain statement c is correct or not on the basis of given information.

The statement is correct because there is 95%confidence that population mean lie between 26.2and27.4.

The exact value is not known, so it can be any value between 26.2and27.4

The statement is correct.

05

To Explain statement d is correct or not on the basis of given information.

There will be no change in population mean. I will be value between 26.2and27.4.

That is, 100%or 0%of time.

So, the statement is incorrect.

06

To Explain statement e is correct or not on the basis of given information. 

It is incorrect as there are 95%of samples has 95%confidence interval having true population mean.

So,(26.2,27.4)may be among remaining5%samples not having true population mean.

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