Question

Victoria’s Secret online offers 2,500 items for sale, 60 of them are offered to VIP’s only. Fredricks of Hollywood offers 1,300 items, where 45 are available to VIP members only. I believe that the proportion of VIP only items on the Fredricks website is more than the proportion of VIP items on the VS website.

Gather appropriate data and post the solution to compare these two proportions.

Answer 1

Let p1 = The population proportion of items offered to VIP's on Fredricks website

Let p2 = The population proportion of items offered to VIP's on VS website

= The sample proportion of items offered to VIP's on Fredricks website = 45/1300 = 0.0346

= The sample proportion of items offered to VIP's on VS website = 60/2500 = 0.024

Let = Overall proportion = (60+45)/2500+1300) = 105/3800 = 0.0276

1 - = 0.9724

= Default level (as nothing is mentioned) = 0.05

(a) The Hypothesis:

H0: p₁ = p₂ : The proportion of items offered to VIP's on Fredrick's website is equal to the proportion of items offered to VIP's on VS website.

Ha: p₁ > p₂ : The proportion of items offered to VIP's on Fredrick's website is greater than the proportion of items offered to VIP's on VS website.

This is a Right Tailed Test.

The Test Statistic:

The p Value: The p value (Right Tail) for Z = 1.89, is; p value = 0.0294

The Critical Value: The critical value (Right tail) at = 0.05, Zcritical = + 1.645

The Decision Rule:    

Critical Value Method: If Zobserved is > Zcritical

P-Value Method: If the P value is < , Then Reject H0

The Decision:   

Critical Value Method: Since Z observed (1.89) is > Zcritical (1.645), We Reject H0.

P-Value Method: Since P value (0) is < (0.05), We Rejec H0.

The Conclusion: There is sufficient evidence at the 95% significance level to conclude that the proportion of items offered to VIP's on Fredrick's website is greater than the proportion of items offered to VIP's on VS website.