Question

For a hypothesis test of H0: p = 0.40 against the alternative Ha: p > 0.40, the z test statistic is found to be 2.25. What can be said about this finding?


a. The finding is significant at both α = 0.05 and α = 0.01.

b. The finding is significant at α = 0.05 but not at α = 0.01.

c. The finding is significant at α = 0.01 but not at α = 0.05.

d. The finding is not significant at α = 0.05 and α = 0.01.

e. The finding is inconclusive because we don't know the value of p-hat.

Answer 1

Answer:

B

Step-by-step explanation:

The first thing we need to do here is to find the probability value that corresponds to z-score of 2.25

While this is traceable using the normal distribution table, we can easily find it using the Normal distribution function in excel

By using this, we get the probability P value of the z score 2.25 to be 0.012224

Now, before we can accept or reject H0, we need to compare the value of P to the significance level alpha

If P ≤ alpha, we reject the null hypothesis H0

At alpha = 0.05, p value is lesser , we reject the null hypothesis.

At alpha P 0.01, p value is greater so we accept null hypothesis

This shows that the finding is significant at alpha = 0.05 (since we rejected null hypothesis) but not at alpha = 0.01(since we accepted null hypothesis)

Answer 2

the The finding should be option b. The finding is significant at α = 0.05 but not at α = 0.01.

Calculation of the probability value:

Since the z test statistic is found to be 2.25.

Now the P value of the z score 2.25 to be 0.012224

In the case when P ≤ alpha, we reject the null hypothesis H0

Now

At alpha = 0.05, the p-value is lesser, we reject the null hypothesis.

At alpha P 0.01, p value is more so we accept null hypothesis

Therefore, the option b is correct.

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