Question

A 90% confidence interval is created for the proportion of consumers which prefer your product over the competitors. This interval is found to be 46% to 64%. a. Using this interval, is it correct to say with 90% confidence that more consumers prefer your product? Explain your reasoning. You are a dishonest statistician and want to ensure that you can say more consumers prefer your product than they do a competitor’s b. What are two ways that you can manipulate these results to get a more favorable outcome which according to the data is statistically correct, (i.e. not just lying)?

Answer 1

a) As 50% lies inside the confidence interval, and the whole confidence interval does not lie above 50%, from the given confidence interval, we dont have sufficient evidence that more consumer prefer our product.

b) We can either manipulate the results by

• decreasing the confidence level of our analysis, for example doing a test at 80% confidence level which might give a confidence interval all above 50% and show that our product is more effective.
• Another way is to increase the sample size for the analysis which will deacrease the margin of error and hence the confidence interval width decreases and possibly bring it above 50%.