Question

he 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 47 male consumers was $135.67, and the average expenditure in a sample survey of 37 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $36, and the standard deviation for female consumers is assumed to be $22.

Answer 1

Male and female consumers differ in the amounts they spend

Step-by-step explanation:

Null hypothesis: Male and female consumers do not differ in the amounts they spend

Alternate hypothesis: Male and female consumers differ in the amounts they spend

Z = (sample mean - population mean)/(sd/√n)

Male consumers

Z = (135.67 - 100.89)/(36/√47) = 34.78/5.25 = 6.62

Female consumers

Z = (68.64 - 100.89)/(22/√37) = -32.25/3.62 = -8.91

Assuming a 5% significance level and two tailed test

To obtain the critical value of a two tailed test, divide the significance level by 2. The critical value is 1.96 from the standard normal distribution table.

For a two tailed test, the region of no rejection of the null hypothesis lies between -1.96 and 1.96.

-8.91 and 6.62 fall outside the region bounded by -1.96 and 1.96, so we reject the null hypothesis.

Male and female consumers differ in the amounts they spend