Question

8. A sample of n = 4 individuals is selected from a normal population with m = 70 and s = 10. A treatment is administered to the individuals in the sample, and after the treatment, the sample mean is found to be M = 75.

A. On the basis of the sample data, can you conclude that the treatment has a significant effect? Use a two-tailed test with a = .05.

B. Suppose that the sample consisted of n = 25 individuals and produced a mean of M = 75. Repeat the hypothesis test at the .05 level of significance.

C. Compare the results from part (a) and part (b). How does the sample size influence the outcome of a hypothesis test?

Your answers for (A), (B), and (C) respectively are

a.       N.S. (meaning "Not Significant"); significant; larger n means MORE likely to be significant

b.      significant; N.S.; larger n means MORE likely to be significant

c.       N.S.; significant; larger n means LESS likely to be significant

d.      significant; N.S.; larger n means LESS likely to be significant

9. A researcher would like to determine whether there is any relationship between students’ grades and where they choose to sit in the classroom. Specifically, the researcher suspects that the better students choose to sit in the front of the room. To test this hypothesis, the researcher asks her colleagues to help identify a sample of n = 100 students who all sit in the front row in at least one class. At the end of the semester, the grades are obtained for these students and the average grade point average is M = 3.25. For the same semester, the average grade point average for the entire college is m = 2.95 with s = 1.10. Use a two-tailed test with a = .01 to determine whether students who sit in the front of the classroom have significantly different grade point averages than other students.

NOTICE that you are asked to use a = .01!

a.       sig., p<.01

b.      N.S. ("not significant"), p>.01

c.       sig., p>.01

d.      N.S., p<.01

Answer 1

8. (A)

The null and alternative hypothesis

Test statistic ,

= (75-70) / (10/2)

= 1

At a =0.05 , critical value of z is 1.96 (two tailed)

Since Calculated z < z- critical ,the result is not significant

we fail to reject H0.

There is not sufficient evidence to conclude that treatment has significant effect .

(B)

Test statistic ,

=(75-70) / (10/5)

= 2.5

At a =0.05 , critical value of z is 1.96 (two tailed)

Since Calculated z > z- critical , the result is significant

we reject H0.

There is sufficient evidence to conclude that treatment has significant effect .

(C) Answer is

(b) NS , Significant , larger n means more likely to be significant .

9.

The null and alternative hypothesis

Test statistic ,

= (3.25-2.95) / (1.10/ 10)

= 2.73

At a =0.01 , critical value of z is 2.58 (two tailed)

Since Calculated z >  z- critical , the result is significant .

P value = 0.0063 < 0.01, the result is significant

Answer : Significant , p < 0.01