A researcher is investigating the effectiveness of a new study-skills training p

Question

A researcher is investigating the effectiveness of a new study-skills training program for elementary school children. A sample of n = 64 third-grade children is selected to participate in the program and each child is given a standardized achievement test at the end of the year. For the regular population of third-grade children, scores on the test form

a normal distribution with a mean of µ = 150 and a standard deviation of = 22. The mean for the sample is M = 156.

            a.         Identify the independent and the dependent variables for this study.

            b.         Assuming a two-tailed test, state the null hypothesis in a sentence that includes

                        the independent variable and the dependent variable.

c.         Using symbols, state the hypotheses (H0 and H1) for the two-tailed test.

d.         Calculate the test statistic (z-score) for the sample.

Explanation / Answer

A researcher is investigating the effectiveness of a new study-skills training program for elementary school children. A sample of n = 64 third-grade children is selected to participate in the program and each child is given a standardized achievement test at the end of the year. For the regular population of third-grade children, scores on the test form a normal distribution with a mean of µ = 150 and a standard deviation of = 22. The mean for the sample is M = 156.

a.               Identify the independent and the dependent variables for this study.

The dependent variable for this study is given as the effectiveness of a new study skills training program and the independent variable is the score of the student in the third grade.

b.              Assuming a two-tailed test, state the null hypothesis in a sentence that includes the independent variable and the dependent variable.

Here we have to use the one sample t test for checking the given claim. The null and alternative hypothesis for this two tailed test is given as below:

Null hypothesis: H0: The average score of a standardized achievement test of the third grade children is 150.

Alternative hypothesis: Ha: The average score of a standardized achievement test of the third grade children is not 150.

c.               Using symbols, state the hypotheses (H0 and H1) for the two-tailed test.

Symbolically, the null and alternative hypothesis for this test is given as below:

H0: µ = 150 versus Ha: µ 150

d.              Calculate the test statistic (z-score) for the sample.

The formula for the test statistic z is given as below:

Z = (sample mean – population mean) / [population standard deviation / sqrt (n)]

Z = (xbar - µ) / [/sqrt (n)]

Z = (156 – 150) / [22 / sqrt (64)]

Z = 2.181818

Test statistic = Z = 2.181818

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