Question

Refer to the random sample of customer order totals with an average of $78.25 and a population standard deviation of $22.50.

a. Calculate percent 90 confidence interval estimate of the mean, given a sample size of 40 orders.

b. Calculate 9 0 percent confidence interval for the mean, given the sample size of 75 orders.

c. Explain the difference.

d. Calculate the minimum sample size needed to identify a %90 confidence interval for the mean, assuming a $5.00 margin of error.

Answer 1

Given:

= $78.25, = $22.50

a) For, n = 40

Critical value:

Z /2 = Z0.10/2 = 1.645          ...................Using standard Normal table

90% Confidence Interval:

b) For, n = 75

Critical value:

Z /2 = Z0.10/2 = 1.645          ...................Using standard Normal table

90% Confidence Interval:

C)

If Increases the sample size 40 to 75, Then Standard error decrease as well as Margin of error decrease. Therefore,

A 95% Confidence interval with n = 75 will be narrower than a 95% Confidence interval with n = 40

D)

Sample size: