You need to compute a 99% confidence interval for the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 3.2? (Use 12.8 as an estimate of the population standard deviation from prior studies.) Use Table 1. (Round intermediate calculations to 4 decimal places and "z" value to 2 decimal places. Round up your answer to the nearest whole number.)

Sample size ___

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 22, 23, 14, 24, 18, 16, 15, 12. Use Table 2.

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

Sample mean__
Sample standard deviation__

b.
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 __

c.
Construct the 99% 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 90% to 99%?

1.As the confidence level increases, the interval becomes narrower.

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