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A newspaper reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was $137.67, and the average expenditure in a sample survey of 30 female consumers was $65.64. Based on past surveys, the standard deviation for male consumers is assumed to be $45, and the standard deviation for female consumers is assumed to be $20.
A) What is the point estimate (in dollars) of the difference between the population mean expenditure for males and the population mean expenditure for females?
B) At 99% confidence, what is the margin of error (in dollars)? (Round your answer to the nearest cent.
C) Develop a 99% confidence interval (in dollars) for the difference between the two population means.

Answer 1

The point estimate of the difference between the population mean expenditure for males and females is $72.03. The margin of error is $20.41. The 99% confidence interval is ($51.62, $92.44).

Step-by-step explanation:

To find the point estimate of the difference between the population mean expenditure for males and females, subtract the average expenditure for females from the average expenditure for males.

Point estimate = Mean expenditure for males - Mean expenditure for females = $137.67 - $65.64 = $72.03

To find the margin of error, use the formula: Margin of error = critical value * standard error.

Standard error = √[(standard deviation for males)^2 / sample size for males + (standard deviation for females)^2 / sample size for females] = √[(45)^2 / 40 + (20)^2 / 30] = 7.93

Using a 99% confidence level, the critical value is approximately 2.576.

Margin of error = 2.576 * 7.93 = 20.41

Finally, to find the confidence interval, subtract and add the margin of error to the point estimate.

Confidence interval = Point estimate ± Margin of error = $72.03 ± 20.41 = ($51.62, $92.44)