Posted by Adam on Wednesday, March 23, 2011 at 2:01am.
A research manager at CocaCola claims that the true proportion, p, of cola drinkers that prefer
CocaCola over Pepsi is greater than 0.50. In a consumer taste test, 100 randomly selected people
were given blind samples of CocaCola and Pepsi. 58 of these subjects preferred CocaCola. Is there
sufficient evidence at the 5% level of significance to validate CocaCola’s claim? Conduct an
appropriate hypothesis test using (i) the pvalue method and (ii) the critical value method.

Statistics and Probability  MathGuru, Wednesday, March 23, 2011 at 7:09pm
Null hypothesis:
Ho: p = .50 >meaning: population proportion is equal to .50
Alternative hypothesis:
Ha: p > .50 >meaning: population proportion is greater than .50
Using a formula for a binomial proportion onesample ztest with your data included, we have:
z = .58  .50 >test value (58/100 = .58) minus population value (.50)
divided by
√[(.50)(.50)/100]
Using a ztable, find the critical or cutoff value for a onetailed test (upper tail) at .05 level of significance. The test is onetailed because the alternative hypothesis is showing a specific direction (greater than).
The pvalue will be the actual level of the test statistic. You can use a ztable to determine that value.
I hope this will help get you started.