Question

1. A researcher is interested in comparing a new self-paced method of teaching statistics with the traditional method of conventional classroom instruction. On a standardized test of knowledge of statistics, the mean score for the population of students receiving conventional classroom instruction is μ = 60. At the beginning of the semester, she administers a standardized test of knowledge of statistics to a random sample of 30 students in the self-paced group and finds the group mean is

M = 55 and s = 14. Assume you wish to determine whether the performance for the self-paced group differs significantly from the performance of those students enrolled in courses offering conventional classroom instruction.

a. State the null hypothesis.

b. Make a diagram of the regions of acceptance and rejection associated with the null hypothesis and label the horizontal axis in terms of values of the t-statistic. Use alpha = .05, two tailed test.

c. Calculate the value of the t-statistic associated with the sample mean of M = 55.

d. Make your decision to reject and retain and describe what this means.

Answer 1

a.

Null Hypothesis H0: Mean score of students enrolled iin self-paced group is equal to the mean score for the population of students receiving conventional classroom instruction which is 60. That is = 60

Alternative Hypothesis Ha: Mean score of students enrolled iin self-paced group is not equal to the mean score for the population of students receiving conventional classroom instruction which is 60. That is 60

b.

Degree of freedom = n-1 = 30-1 = 29

Critical value of t statistic at alpha = .05 and df = 29 is  2.05

The shaded region (t < -2.05 or t > 2.05) is rejection region associated with the null hypothesis.

The unshaded region (-2.05 < t < 2.05) is acceptance region associated with the null hypothesis.

c.

Standard error of mean = s/ = 14 / = 2.556

Test Statistic, t = (M - ) / SE = (55 - 60) / 2.556 = -1.96

d.

Since the value of test statistic does not lie in the rejection region, we fail to reject null hypothesis H0 and conclude that there is no strong evidence to believe that the score of students enrolled iin self-paced group is not equal to the mean score for the population of students receiving conventional classroom instruction which is 60.