Question

Our friend the waffle-man is back and wants to do more hypothesis tests for proportions, but this time for four waffle recipes. He randomly selected 250 waffle consumers and found that 100 (40%) of the 250 preferred Waffle No. 2. He conducted a hypothesis test with

H0:p=0.25H0:p=0.25, Ha:p>0.25Ha:p>0.25.

Notice the proportion under the null distribution is p_0 = 0.25. The test statistic for this problem is 5.47. You can verify for yourself that the probability of observing this test statistic is nearly zero assuming the null hypothesis is true.

Now suppose we wish to conduct the same hypothesis test again if the true proportion is 0.35. In other words, we happen to know the true parameter value is 0.35, something that is typically not known. How does the test statistic change with this new information? What is the resulting p-value?

Hint: Try writing what the null hypothesis and test statistic would be given this new information. What would change, if anything?

Select one:

a. The test statistic becomes 1.61 with a p-value of 0.537.

b. The test statistic becomes 1.66 with a p-value of 0.095.

c. The test statistic becomes -3.23 with a p-value of 0.9995.

d. The test statistic does not change from its original value of 5.47, and the associated p-value does not change.

e. None of the other answers are correct.

Answer 1