Posted by Bettie on .
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.

STATISTICS 
MathGuru,
Using a formula for a binomial proportion onesample ztest with your data included, we have:
z = .62  .50 / √[(.50)(.50)/50]
Finish the calculation.
Use a ztable to find the critical or cutoff value at 0.01 for a onetailed test.
If the ztest statistic calculated above exceeds the critical value from the ztable, reject the null. If the ztest statistic does not exceed the critical value from the ztable, do not reject the null.
I hope this will help get you started.