## A Large Public Utility Wishes To Compare The Consumption

1. A large public utility wishes to compare the consumption of electricity during the summer season for single- family homes in two of the counties that it services. A random sample of 10 households in County A yielded a mean monthly bill of $125 with a standard deviation of $32, while a sample of 9 households in County B yielded a mean monthly bill of $108 with a standard deviation of $16.(a) Calculate the ratio of the maximum sample variance to the minimum sample variance. Does it appear that the population variances are equal or unequal? Explain.(b) Construct the appropriate 90% confidence interval for the difference in the mean monthly bills for single-family homes in the two counties, and interpret the result. Be sure to clearly define the two populations of interest, and state any assumptions necessary to validate your interval.(c) Based on your interval in (b), does there appear to be a difference in the mean monthly bills in the two counties? Why?(d) Suppose that the means and standard deviations above were based on samples of 150 households selected from each county (instead of on samples of sizes 11 and 10). Construct the appropriate 90% confidence interval for the difference in mean monthly bills. Does there now appear to be a difference in the means? Comment on the benefits achieved by increasing the sample sizes.(e) Are the assumptions necessary to validate the intervals in (b) and (d) the same? Explain.

## A large public utility wishes to compare the consumption

Question

1. A large public utility wishes to compare the consumption of electricity during the summer season for single- family homes in two of the counties that it services. A random sample of 10 households in County A yielded a mean monthly bill of $125 with a standard deviation of $32, while a sample of 9 households in County B yielded a mean monthly bill of $108 with a standard deviation of $16.

(a) Calculate the ratio of the maximum sample variance to the minimum sample variance. Does it appear that the population variances are equal or unequal? Explain.

(b) Construct the appropriate 90% confidence interval for the difference in the mean monthly bills for single-family homes in the two counties, and interpret the result. Be sure to clearly define the two populations of interest, and state any assumptions necessary to validate your interval.

(c) Based on your interval in (b), does there appear to be a difference in the mean monthly bills in the two counties? Why?

(d) Suppose that the means and standard deviations above were based on samples of 150 households selected from each county (instead of on samples of sizes 11 and 10). Construct the appropriate 90% confidence interval for the difference in mean monthly bills. Does there now appear to be a difference in the means? Comment on the benefits achieved by increasing the sample sizes.

(e) Are the assumptions necessary to validate the intervals in (b) and (d) the same? Explain.

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