A local donut shop wishes to test out its donuts against those of the competition which is planning to set up in the community. Each of 50 subjects tastes 2 unidentified donuts and says which they perfer. 31 or 62% of the subjects perfer the local company's donuts to the competition's donuts. Test the claim that a majority(over 50%) of people prefer the local company donuts at the significance level of 0.01. What is your practical conclusion? Do a full hypotheses test.

Question

A local donut shop wishes to test out its donuts against those of the competition which is planning to set up in the community. Each of 50 subjects tastes 2 unidentified donuts and says which they perfer. 31 or 62% of the subjects perfer the local company's donuts to the competition's donuts. Test the claim that a majority(over 50%) of people prefer the local company donuts at the significance level of 0.01. What is your practical conclusion? Do a full hypotheses test.
Suggest how you would design and conduct this experiment.

MathGuru · Answer

Using a formula for a binomial proportion one-sample z-test with your data included, we have:

z = .62 - .50 / √[(.50)(.50)/50]

Finish the calculation.

Use a z-table to find the critical or cutoff value at 0.01 for a one-tailed test.

If the z-test statistic calculated above exceeds the critical value from the z-table, reject the null. If the z-test statistic does not exceed the critical value from the z-table, do not reject the null.

I hope this will help get you started.