# Estimating Population Values

7.14

The First National bank is considering a survey of its customers to estimate the man number of checks written per month. A sample of 360 customers was selected. The sample values were _

X = 33.4

S = 11.2

a. Provide a 90% confidence interval estimate for the mean number of checks written and interpret the estimate.

b. Suppose a clerical mistake was made in recording the number of customers who were surveyed and the actual sample size was 36, not 360. Re compute the 90% confidence interval estimate and compare it to the estimate developed in a part a. Why the estimates are different even thought the sample mean and standard deviation did not change

7.11

Mortimor's is a nice, upscale restaurant specializing in seafood dishes. The owner is interested in estimating the mean dollars spent per table on appetizers. He has selected a simple random sample of 200 sales receipts from the past year's receipts and has calculated the mean and standard deviation for the dollar amount of each bill that was allocated to appetizers. These results are:

_

X = $4.22 s = $2.59

a. Based on these sample dat6a, what is the point estimate for the mean amount spent on appetizers per table at Mortimer's?

b. Construct and interpret a 95% confidence interval estimate for the true mean amount spent per table on appetizers.

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#### Solution Preview

7.14 The First National bank is considering a survey of its customers to estimate the man number of checks written per month. A sample of 360 customers was selected. The sample values were _

X = 33.4

S = 11.2

a. Provide a 90% confidence interval estimate for the mean number of checks written and interpret the estimate.

b. Suppose a clerical mistake was made in recording the number of customers who were surveyed and the actual sample size was 36, not 360. Re compute the 90% confidence interval estimate and compare it to the estimate developed in a part a. Why the estimates are different even thought the sample mean and standard deviation did not change

Answer

a. Provide a 90% confidence interval estimate for the mean number of checks written and interpret the estimate.

The 90% Confidence Interval is given by . Where represent the significance level ( here = 0.1). Where , is the sample mean ...

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