Question

How much customers buy is a direct result of how much time they spend in the store. A study of average shopping times in a large national houseware store gave the following information (Source: Why We Buy: The Science of Shopping by P. Underhill).

Women with female companion: 8.3 min.
Women with male companion: 4.5 min.

Suppose you want to set up a statistical test to challenge the claim that a woman with a female friend spends an average of 8.3 minutes shopping in such a store.

(a) What would you use for the null and alternate hypotheses if you believe the average shopping time is less than 8.3 minutes?

H_o: ? = 8.3; H₁: ? < 8.3

H_o: ? = 8.3; H₁: ? > 8.3

H_o: ? < 8.3; H₁: ? = 8.3

H_o: ? = 8.3; H₁: ? ? 8.3

Is this a right-tailed, left-tailed, or two-tailed test?

(b) What would you use for the null and alternate hypotheses if you believe the average shopping time is different from 8.3 minutes?

H_o: ? ? 8.3; H₁: ? = 8.3

H_o: ? = 8.3; H₁: ? ? 8.3    

H_o: ? = 8.3; H₁: ? > 8.3

H_o: ? = 8.3; H₁: ? < 8.3

Is this a right-tailed, left-tailed, or two-tailed test?

Stores that sell mainly to women should figure out a way to engage the interest of men! Perhaps comfortable seats and a big TV with sports programs. Suppose such an entertainment center was installed and you now wish to challenge the claim that a woman with a male friend spends only 4.5 minutes shopping in a houseware store.

(c) What would you use for the null and alternate hypotheses if you believe the average shopping time is more than 4.5 minutes?

H_o: ? = 4.5; H₁: ? > 4.5

H_o: ? = 4.5; H₁: ? < 4.5   

H_o: ? = 4.5; H₁: ? ? 4.5

H_o: ? > 4.5; H₁: ? = 4.5

Is this a right-tailed, left-tailed, or two-tailed test?

(d) What would you use for the null and alternate hypotheses if you believe the average shopping time is different from 4.5 minutes?

H_o: ? = 4.5; H₁: ? < 4.5

H_o: ? = 4.5; H₁: ? > 4.5    

H_o: ? = 4.5; H₁: ? ? 4.5

H_o: ? ? 4.5; H₁: ? = 4.5

Is this a right-tailed, left-tailed, or two-tailed test?

Answer 1

(a) Average shopping time is less than 8.3 minutes - - Option 1

H0: $\mu$ = 8.3

H1: $\mu$ < 8.3

This is a left tailed test.

(b) Average shopping time is different from 8.3 minutes - - Option 2

H0: $\mu$ = 8.3

H1: $\mu$ $\ne$ 8.3

This is a two tailed test.

(c) Average shopping time is less than 4.5 minutes - - Option 1

H0: $\mu$ = 4.5

H1: $\mu$ > 4.5

This is a right tailed test.

(d) Average shopping time is different from 4.5 minutes - - Option 3

H0: $\mu$ = 4.5

H1: $\mu$ $\ne$ 4.5

This is a two tailed test.