2. Montarello and Martins (2005) found that fifth-grade students completed more

Question

2. Montarello and Martins (2005) found that fifth-grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of = 100 and a standard deviation of = 18. The researcher modifies the test by inserting a set of easy problems among the standardized questions, and gives the modified test to a sample of n = 36 students. If the average test score for the sample is M = 104, is this result sufficient to conclude that inserting the easy questions improves student performance? Use a one-tailed test with = .01. (Use 2 decimal places.)

z-critical =

z=

Conclusion

Reject the null hypothesis, there is not a significant increase in student performance.

Fail to reject the null hypothesis, there is not a significant increase in student performance.    

Reject the null hypothesis, there is a significant increase in student performance.

Fail to reject the null hypothesis, there is a significant increase in student performance.

Explanation / Answer

For one-tailed (right tailed) test at alpha=0.01, z critical is 2.326.

From information given, Xbar=104 and mu=100, sigma=18, n=36. Substitute the values in following equation to obtain the z score.

z=(Xbar-mu)/(sigma/sqrt n)=(104-100)/(18/sqrt 36)=1.33.

The test statistic do not fall in critical zone, therefore, fail to reject null hypothesis. Therefore, conclude that there is not sufficient sample evidence to ocnclude that there is significant increase in students' performance. Option B.

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