Question

a study was done using a treatment group and a placebo group. the results are shown in the table. assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. use a 0.10 significance level to answer the questions below.

the test statistic, t, is -1.58. (round to two decimal places as needed.)

the p - value is 0.120. (round to three decimal places as needed.)

state the conclusion for the test.

a. fail to reject the null hypothesis. there is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

b. reject the null hypothesis. there is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

c. reject the null hypothesis. there is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

d. fail to reject the null hypothesis. there is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

Explanation:

Step1: Recall the decision rule for hypothesis testing

If the P - value > significance level ($\alpha$), we fail to reject the null hypothesis. Here, $\alpha = 0.10$ and the P - value is $0.120$.

Step2: Compare the P - value and the significance level

Since $0.120>0.10$ (i.e., P - value > $\alpha$).

Answer:

D. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.