Question

A yogurt company claims that it prints a free yogurt coupon under a randomly selected 20% of its lids. A loyal customer purchases 85 yogurt cups, and records whether each was a winner. After consuming all 85 cups, he is disappointed to see that only 12 (14.1%) of his yogurt cups contained coupon codes. He performs a 99% confidence interval for the proportion of yogurt cups containing coupon codes, obtaining (0.044, 0.238). What conclusion can the customer draw about the yogurt company’s claim?

Answer 1

Answer:

The customer can conclude that the company's claim is correct

Step-by-step explanation:

The percentage of lids that has a free yogurt coupon = 20%

The number of cups a loyal customer purchases = 85 yogurt cups

The number of cups that contained a coupon = 12 (14.1%)

The confidence interval performed = 99% confidence interval for the proportion of yogurt cups containing coupon codes

The interval obtained = (0.044, 0.238)

Therefore, the range of proportion within which the true proportion exists is 0.044 < $\hat p$ < 0.238

The range of percentage within which the true percentage exist is therefore;

0.044 × 100 = 4.4%  < $\hat p$ × 100 < 0.238 × 100 = 23.8%

Given that the possible true percentage of lids that has a coupon is between 4.4% and 23.8% at 99% confidence level, the customer can conclude that only 12 of his yogurt cup contained coupon by chance and that the company's claim is correct.