Question

The average expenditure on Valentine's Day was expected to be $100.89 (USA Today, February 13, 2006). Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 60 male consumers was $134.44, and the average expenditure in a sample survey of 33 female consumers was $63.97. Based on past surveys, the standard deviation for male consumers is assumed to be $31, and the standard deviation for female consumers is assumed to be $20. The z value is 2.576.

Answer 1

Ho : 1 = 2

Ha : 1 2

Test statistic Z = 2.576

critical value Zcritical = Z_{​​​​​a/2} = Z_{​​​​​​0.025}

Zcritical = 1.96

Decision rule : Reject Ho if Z >1.96

So Z = 2.576 > 1.96

Decision : we reject the null hypothesis Ho

Conclusion : There is sufficient evidence to support the claim that male and female consumers differ in the amounts they spend