Question

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 25, 11, 12, 27, 26, 22, 8, 5. Use Table 2.

a. Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places. Round "Sample mean" to 3 decimal places and "Sample standard deviation" to 2 decimal places.)

Sample mean
Sample standard deviation

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

Confidence interval             to

c. Construct the 90% confidence interval for the population mean. (Round "t" value to 3 decimal places and final answers to 2 decimal places.)

Confidence interval             to

d. What happens to the margin of error as the confidence level increases from 95% to 90%?

	As the confidence level increases, the margin of error becomes smaller.
	As the confidence level increases, the margin of error becomes larger.

Answer 1

Solution: a. Calculate the sample mean and the sample standard deviation.

Answer:

Sample standard deviation is given below:

  

Sample standard deviation

  

b. Construct the 95% confidence interval for the population mean.

Answer: The 95% confidence interval for the population mean is given below:

Where

  

  

95% confidence interval is to

c. Construct the 90% confidence interval for the population mean.

Answer: The 90% confidence interval for the population mean is given below:

Where

  

  

90% confidence interval is to

d. What happens to the margin of error as the confidence level increases from 95% to 90%?

Answer: As the confidence level increases, the margin of error becomes larger.