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: μ = 8.3; H₁: μ > 8.3

H_o: μ = 8.3; H₁: μ < 8.3  

  H_o: μ = 8.3; H₁: μ ≠ 8.3

H_o: μ < 8.3; H₁: μ = 8.3

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

left-tailed

two-tailed   

right-tailed

(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: μ ≠ 8.3; H₁: μ = 8.3

H_o: μ = 8.3; H₁: μ < 8.3  

H_o: μ = 8.3; H₁: μ ≠ 8.3

H_o: μ = 8.3; H₁: μ > 8.3

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

two-tailed

right-tailed

left-tailed

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: μ > 4.5; H₁: μ = 4.5

H_o: μ = 4.5; H₁: μ < 4.5    

H_o: μ = 4.5; H₁: μ > 4.5

H_o: μ = 4.5; H₁: μ ≠ 4.5

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

right-tailed

two-tailed   

left-tailed

(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: μ = 4.5; H₁: μ ≠ 4.5

H_o: μ = 4.5; H₁: μ < 4.5   

H_o: μ = 4.5; H₁: μ > 4.5

H_o: μ ≠ 4.5; H₁: μ = 4.5

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

two-tailed

left-tailed

right-tailed

Answer 1

Solution :

(a)

H_o: μ = 8.3; H₁: μ < 8.3  

left-tailed

(b)

H_o: μ = 8.3; H₁: μ ≠ 8.3

two-tailed

(c)

H_o: μ = 4.5; H₁: μ > 4.5

right-tailed

(d)

H_o: μ = 4.5; H₁: μ ≠ 4.5

two-tailed