Question

A researcher administers a treatment to a sample of n = 25 participants and uses a hypothesis test to evaluate the effect of the treatment. The hypothesis test produces a z-score of z = 2.77.
1. Assuming that the researcher is using a two-tailed test _________.
a. The researcher rejects the null hypothesis with a = .05 but not with a = .01.
b. The researcher should reject the null hypothesis with either a = .05 or a = .01.
c. The researcher should fail to reject H0 with either a = .05 or a = .01.
d. Cannot answer without additional information.

Answer 1

Answer:

Option b: The researcher should reject the null hypothesis with either a = 0.05 or a = 0.01.

Step-by-step explanation:

We are given that a researcher administers a treatment to a sample of n = 25 participants and uses a hypothesis test to evaluate the effect of the treatment. The hypothesis test produces a z-score of z = 2.77.

Also, it is assumed that the researcher is using a two-tailed test.

Now, firstly we will find the critical value of z at significance level $(\alpha)$ 0.05 and 0.01.

Our decision rule will be ;

• If the value of z score is more than the critical values of z, then we will reject null hypothesis.

• If the value of z score is less than the critical values of z, then we will not reject null hypothesis.

So, at 0.05 significance level z table gives critical value of 1.96.

and at 0.01 significance level z table gives critical value of 2.5758.

As we can clearly see that our z score is more than both the critical values of z at significance level 0.05 and 0.01 so we have sufficient evidence to reject null hypothesis at both significance level.

Hence, the researcher should reject the null hypothesis with either a = 0.05 or a = 0.01.

Answer 2

Answer: option B

Step-by-step explanation: at alpha level of 5% for a two tailed test, the critical value is +1.96 and -1.96

At alpha level of 1% for a two tailed test, the critical value is +2.576 and -2.576

Relating z = 2.77 with these critical values, we can see that at 5% level of significance, z = 2.77 is greater than +1.96 which falls in the rejection region.

Also at 1% level of significance, we can see that z = 2.77 is greater than 2.576 which also falls in the rejection region.