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91影视

17. Explaining confidence A 95%confidence interval for the mean body mass index (BMI)of young American women is 26.80.6. Discuss whether each of the following explanations is correct.
(a) We are confident that 95%of all young women have BMIbetween 26.2and 27.4.
(b) We are 95%confident that future samples of young women will have mean BMIbetween 26.2and 27.4.
(c) Any value from 26.2to 27.4is believable as the true mean BMI of young American women.
(d) In 95%of all possible samples, the population mean BMIwill be between 26.2and 27.4.
(e) The mean BMIof young American women cannot be 28.

Short Answer

Expert verified

(a) The explanation that 95%confident of all young women have mean BMIbetween 26.2and 27.4is incorrect.

(b) The explanation that 95%confident that future samples of young women will have mean BMIbetween 26.2and 27.4is incorrect.

(c) The explanation that any value from 26.2to 27.4is believable as the true mean BMIof young American women is correct.

(d) The explanation that in 95%of all possible samples, the population mean BMIwill be between 26.2and 27.4is incorrect.

(e) The explanation that the mean BMIof young American women cannot be 28 is incorrect.

Step by step solution

01

Part (a) Step 1: Given information

To determine whether the statement that 95%of all young women have BMIbetween26.2and 27.4is correct or not.

02

Part (a) Step 2: Explanation

Let, the Confidence interval is 95%
And the body mass index as:

(BMI)=260.6
Also, 26.2and 27.4
The confidence interval is only stated for young women in this observation, not for individual women.
As a result, explanation (a) is incorrect.

03

Part(b) Step 1: Given information

To determine whether the statement that 95%confident that future samples of young women will have mean BMIbetween 26.2and 27.4is correct or not.

04

Part (b) Step 2: Explanation

Let, the confidence interval is 95%.

And the body mass index is (BMI)=260.6
Also,

26.2 and 27.4.
Because the confidence intervals for future samples may differ.
It's impossible to predict where the true mean BMIwill fall between 26.2 and 27.4.
As a result, explanation (b) is incorrect

05

Part (c) Step 1: Given information

To determine whether the statement that any value from 26.2to 27.4is believable as the true mean BMIof young American women is correct or not.

06

Part (c) Step 2: Explanation

Let the confidence interval is 95%.

And the body mass index is (BMI)=260.6
Also,26.2and 27.4.
The true mean BMIranges from 26.2to 27.4.
As a result, any value between 26.2and 27.4might be considered reasonable as the genuine mean BMI.
As a result, the explanation is correct.

07

Part (d) Step 1: Given information

To determine whether the statement that in 95%of all possible samples, the population mean BMIwill be between 26.2and 27.4is correct or not.

08

Part (d) Step 2: Explanation

Let, the confidence interval is95%.

And the body mass index is (BMI)=260.6
Also,

26.2and 27.4.

The true mean BMIlies between the intervals 26.2and 27.4in the 95 percent confidence interval.
The genuine mean BMIis not present in the remaining 5 percent samples.
As a result, explanation is incorrect.

09

Part(e) Step 1: Given information

To determine whether the statement that the mean BMIof young American women cannot be 28is correct or not.

10

Part (e) Step 2: Explanation

Let, the confidence interval is 95%.

And the Body mass index is (BMI)=260.6
26.2and 27.4
The population mean is unknown in this explanation. As a result, the average BMI may not be equal to 28.
As a result, explanation (e) is incorrect.

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Check conditions for constructing a confidence interval for the parameter

Critical value What critical value t*from Table B would you use for a 90%confidence interval for the population mean based on an SRS of size 77? If possible, use technology to find a more accurate value of . What advantage does the more accurate df provide?

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