The manager of a newly opened gift boutique wants to estimate the average expenditure of his customers using a confidence interval. He estimates that the population standard deviation is approximately $30.50.

(a) For a 98% confidence level, find the appropriate sample size necessary to achieve a margin of error of 7.00.

Determine z2

=

Round your answer (n) UP to the next whole number.

The required sample sizen

is

(b) For a 90% confidence level, find the appropriate sample size necessary to achieve a margin of error of 7.00.

Determine z2

=

Round your answer (n) UP to the next whole number.

The required sample sizen

is

(c) Compare parts (a) and (b). Select the correct statement.

• If the confidence level decreases, then the required sample sizealso decreases.
• If the confidence level decreases, then the required sample sizeincreases.
• If the confidence level decreases, then the required sample sizedoes not change.

(d) Suppose that the confidence level remains invariant. How should we change the sample size to achieve the larger confidence interval?

• Do nothing as the length of the confidence interval does not depend on the sample size.
• Increase the sample size.
• Decrease the sample size.

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