Question

The USA Today 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 49 male consumers was $135.67, and the average expenditure in a sample survey of 40 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $32, and the standard deviation for female consumers is assumed to be $20.

1. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)?
2. At 99% confidence, what is the margin of error (to 2 decimals)?
3. Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.
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Answer 1

Let be the average expenditure by males, be average expenditure by females.

a. Point estimate for the difference in means of two samples is just the difference between the sample means of the two sample. It is 135.67 - 68.64 = 67.03

b. To calculate the margin of error, we need the standard deviation of the joint sample. The standard deviation is calculated as follows:

The critical z value for 99% confidence for a two tailed test is 2.57

Margin of error is:

c. The 99% confidence interval for the difference in population means is calculated as follows:

Since this interval does not contain 0, we reject the null hypothesis and conclude that there is a difference in the average expenditure by males and females.