Asked by Adam
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.
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.
Answers
Answered by
MathGuru
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.
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.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.