Educational testing companies provide tutoring, classroom learning, and practice

Question

Educational testing companies provide tutoring, classroom learning, and practice tests in an effort to help students perform better on tests such as the BECE. The test preparation companies claim that their courses will improve BECE score performances by an average of 120 points. A researcher is uncertain of this claim and believes that 120 points may be an overstatement in an effort to encourage students to take the test preparation course. In an evaluation study of one test preparation service, the researcher collects BECE score data for 35 students who took the test preparation course and 48 students who did not take the course. Students who took test preparation had an average score of 380 points with standard deviation of 10 points and students who did not take the course had an average of 315 points with standard deviation of 18 points.

(a) Formulate the hypotheses that can be used to test the researchers belief that the improvement in BECE scores may be less than the stated average of 120 points.

(b) Using = 0.05, what is your conclusion?

What is the point estimate of the improvement in the average BECE scores provided by the test preparation course? Provide a 95% confidence interval estimate of the improvement.

What advice would you have for the researcher after seeing the confidence interval?

Explanation / Answer

(a) The hypothesis that can be used to test the researchers belief that the improvement in BECE scores may be less than the stated average of 120 points is as follows

H0 : U1-U2 >= 120

Ha: U1-U2 < 120

(b) At the alpha vaue of 0.05 , first we hav to calculate the t statistic as t= U1-U2 / SQRT(s1^2/n1 + s2^2/n2) where U1, U2 are the means of the two populations and s1 and s2 are the std. deviations and n1 and n2 are the sample sizes i.e. t = 380 - 315 / SQRT(10^2/35 + 18^2/48). If the value of the t statistic so calculated gives a p value <0.05 after looking up the std. normal table then we can reject the null hypothesis

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