In a sample of 1000 randomly selected consumers who had opportunities to send in

Question

In a sample of 1000 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product, 250 of these people said they never did so. Reasons cited for their behavior included too many steps in the process, amount too small, missed deadline, fear of being placed on a mailing list, lost receipt, and doubts about receiving the money. Calculate an upper confidence bound at the 95% confidence evel or the true proportion of such consumers who never appl for a rebate. Round your answer for decimal places.) 0.2629 Based on this bound, is there compelling evidence that the true proportion of such consumers is smaller than ? Explain your reasoning. O No, there is not compelling evidence the true proportion is less than-since we can be 95% confident the upper confidence bound is less than O Yes, there is compelling evidence the true proportion is less than we can be 95% confident the upper confidence bound is less than 3 Yes, there is compelling evidence the true proportion is less than since we can be 95% confident the upper confidence bound is greater than No, there is not compelling evidence the true proportion is less than since we can be 95% confident the upp er confidence und is greater than

Explanation / Answer

Solution:- Give that n = 1000 , x = 250
p = x/n = 250/1000 = 0.25 , q = 1-p = 1 - 0.25 = 0.75
95% confidence interval for Z = 1.96
The upper confidence bound at the 95% confidece interval for the true population population = p + Z * sqrt(pq/n)
= 0.25 + 1.96*sqrt(0.25*0.75/1000)
= 0.2768

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