A study was done using a treatment group and a placebo group. The results are sh

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. Complete parts (a) and (b) Use a 0.01 significance level for both parts. Test the claim that the two samples are from populations with the same mean. what are the null and alternative hypotheses? H_0: mu_1=mu_2 H_1:mu_1 > mu_2 H_0: mu_1

Explanation / Answer

State the hypotheses.

The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: 1 - 2 = 0
Alternative hypothesis: 1 - 2 0

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.1934

DF = 62

t = [ (x1 - x2) - d ] / SE

t = - 1.50

where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 40 degrees of freedom is more extreme than -1.5; that is, less than -1.5 or greater than 1.5.

Thus, the P-value = 0.139

Interpret results. Since the P-value (0.139) is less than the significance level (0.01), we cannot accept the null hypothesis.

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