Question

STATISTIC

A company that makes athletic shoes asked a representative sample of its customers whether they preferred the color white or red; 60% of customers in this sample preferred the color red. Separately, a company that makes sparkling water asked a representative sample of its customers to try new flavors: cherry and kiwi; 60% of customers in this sample likewise preferred cherry.

Both companies used a two-sided test with H0: p = .5, and both companies had a sufficiently large sample size to meet the conditions. However, the shoe company used a larger sample of customers.

Which of these studies would have a smaller P-value?
The study about shoe colors
The study about sparkling water flavors    
Both studies have the same P-value
Not enough information is given to determine which P-value is smaller

Answer 1

Both studies used a two-sided test with a null hypothesis of p = 0.5. However, the shoe company used a larger sample size, which would result in a smaller standard error and a more precise estimate of the true proportion.

Assuming that the sample proportions are accurate representations of the true proportions, the study with the larger sample size (the shoe company) would have a smaller P-value. A smaller P-value indicates stronger evidence against the null hypothesis and in favor of the alternative hypothesis that the true proportion is different from 0.5.

Therefore, the study about shoe colors would have a smaller P-value.