Question

A simple random sample with n=54 provided a sample mean of 24.0 and a sample standard deviation of 4.3.

a. Develop a confidence interval for the population mean (to 1 decimal).

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b. Develop a confidence interval for the population mean (to 1 decimal).

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c. Develop a confidence interval for the population mean (to 1 decimal).

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d. What happens to the margin of error and the confidence interval as the confidence level is increased?

- Select your answer -They increase They decrease They stay the same It cannot be determined from the given data The margin of error increases and the confidence interval becomes narrowerThe margin of error decreases and the confidence interval becomes wider .

Answer 1

a)

z value at 90% = 1.645

CI = mean +/- z *(s/sqrt(n))
= 24 +/- 1.645 *(4.3/sqrt(54))
= (23.0375 , 24.9625 )

90% CI = (23.0 , 24.2 )

b)

z value at 95% = 1.96

CI = mean +/- z *(s/sqrt(n))
= 24 +/- 1.96 *(4.3/sqrt(54))
= (22.8531 , 25.1469 )

95% CI = (22.9 , 25.1 )

c)

z value at 99% = 2.576

CI = mean +/- z *(s/sqrt(n))
= 24 +/- 2.576 *(4.3/sqrt(54))
= (22.4927 , 25.5073 )

99% CI = (22.5, 25.5 )

d)
The margin of error increases and the confidence interval becomes narrower