Question

A study was conducted to determine the effectiveness of a certain treatment. A group of 92 patients were randomly divided into an experimental group and a control group. The table shows the result for their net improvement. Let the experimental group be group 1 and the control group be group 2. Experimental Control n 41 51 x overbar 11.2 3.4 s 6.4 6.6 ?(a) Test whether the experimental group experienced a larger mean improvement than the control group at the alpha equals 0.01 level of significance. Should the null hypothesis be? rejected? A. Yes?, because the test statistic is in the critical region. B. Yes?, because the test statistic is not in the critical region. C. No?, because the test statistic is in the critical region. D. No?, because the test statistic is not in the critical region. ?(b) Construct a 95?% confidence interval about mu 1 minus mu 2 and interpret the results. ?Therefore, the confidence interval is the range from nothing to nothing. ?(Round to two decimal places as? needed.) What is the interpretation of this confidence? interval? A. There is a 95?% probability that the difference between randomly selected individuals will be in the interval. B. We are 95?% confident that the difference of the means is in the interval. C. We are 95?% confident that the difference between randomly selected individuals will be in the interval. D. There is a 95?% probability that the difference of the means is in the interval.

Answer 1

Soln,

Given that Samples of 41 of Experimental group 1 and 51 0f control group 2 hence n₁=41 and n₂=51 and also given that

Mean of Samples are 11.2 and 3.4 hence

Also given their standard deviation as S₁=6.4 and S₂=6.2

Now according to question

a) Test the hypotheses at 0.01 level of significance

Hence hypotheses are

Ho :

Ha :

Rejection region :

Reject Ho if Z ( calculated)> Z_0.01=2.32635

or P value<

Hence test staistic used Z test right tail test so,

Hence calculated as Z= 5.729.

Hence p value computed from Z statiostic table as 0.00001 almost is equal to 0.

Hence Conclusion,:

A. yes , because the test statistic is in the critical region.

again according to question.

b) 95 % Confidence interval as

Hence calculated as = 1.3239

and

and

So Confidence interval

Inrerpretation

B. We are 95?% confident that the difference of the means is in the interval.