Question

Treatment Placebo 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. Complete parts (a) and (b) below Use a 0.10 sign ticance level for both parts μι x 2.34 8 0.88 μ2 34 2.65 0.51 a. Test the claim that the two samples are from populations with the same mean What are the null and altemative hypotheses?

A) Test the claim that the two samples are from populations with the same mean.
What are the null and alternative​ hypotheses?

1)P Value

2)Test statistic

3)state the conclusion for the test

b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.

Answer 1

The following null and alternative hypotheses need to be tested This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used (2) Rejection Region Based on the information provided, the significance level is α 0.1, and the degrees of freedom are df 40.987. In fact, the degrees of freedom are computed as follows, assuming that the population variances are unequal Hence, it is found that the critical value for this two-tailed test is te-1.683, for a 40.987 0.1 and df - The rejection region for this two-tailed test is R-t: t>1.683 Since it is assumed that the population variances are unequal, the t-statistic is computed as follow:s n2-1 2 2.34 2.65 1.606 (27-1)0.882+(34-1)0.5421 Since it is observed thatt1.606 rejected te-1.683, it is then concluded that the null hypothesis is not Using the P-value approach: The p-value is p0.1159, and since p that the null hypothesis is not rejected 0.1159 0.1, it is concluded It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ| is different than μ , at the 0.1 significance level. fidence Interval 0.635 <, щ1- 2 < 0.015 The 90% confidence interval is