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.

Treatment ? Placebo?

n 26 39

Xbar 2.36 2.66

S 0.94 0.69

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 0.05 significance level for both parts

(a) Test statistics

(b) p-value

(c) Appropriate confidence Interval

(d) Analysis/Conclusion

Explanation / Answer

Let X represent the treatment group and Y represent the placebo group.

Given data:

Sample mean, X' = 2.36

SX = 0.94

nX = 26

Sample mean, Y' = 2.66

SY = 0.69

nY = 39

Calculating the test statistic as below:

z-score = (Y'-X')/(SX2/nX+ SY2/nY)0.5 = (2.66-2.36)/(0.942/26+ 0.692/39)0.5 = 1.395

p-value for this z-score, assuming a one tailed test = 0.0815

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