A random sample of 26 observations is used to estimate the population mean. The

Question

A random sample of 26 observations is used to estimate the population mean. The sample mean and the sample standard deviation are calculated as 125.4 and 26.50, respectively. Assume that the population is normally distributed. Use Table 2.

Construct the 95% confidence interval for the population mean. (Round intermediate calculations to 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

Construct the 99% confidence interval for the population mean. (Round intermediate calculations to 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

Use your answers to discuss the impact of the confidence level on the width of the interval.

or

2) As the confidence level increases, the interval becomes wider.

Construct the 95% confidence interval for the population mean. (Round intermediate calculations to 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

Explanation / Answer

Answer in detail with explanations:

n= 26

Mean = 125.4
Stdev = 26.50

a. The 95% CI is given by :

Mean +/- t*s/sqrt(N)
=125.4 +/- (2.060*26.5)/(sqrt(26))
=114.69 to 136.11

b. The 99% CI is given by :
Mean +/- t*s/sqrt(N)
=125.4 +/- (2.787*26.5)/(sqrt(26))
=110.92 to 139.88

c. At higher confidence interval we have a wider interval
2) is right

The higher t value insures that margin of error increases, thereby increasing the interval width

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