Homework Help: Statistics and Probability

Posted by Adam on Wednesday, March 23, 2011 at 2:01am.

A research manager at Coca-Cola claims that the true proportion, p, of cola drinkers that prefer
Coca-Cola over Pepsi is greater than 0.50. In a consumer taste test, 100 randomly selected people
were given blind samples of Coca-Cola and Pepsi. 58 of these subjects preferred Coca-Cola. Is there
sufficient evidence at the 5% level of significance to validate Coca-Cola’s claim? Conduct an
appropriate hypothesis test using (i) the p-value 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 one-sample z-test 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 z-table, find the critical or cutoff value for a one-tailed test (upper tail) at .05 level of significance. The test is one-tailed because the alternative hypothesis is showing a specific direction (greater than).

The p-value will be the actual level of the test statistic. You can use a z-table to determine that value.

I hope this will help get you started.

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