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 µ= 100 and a standard deviation of σ = 18. The researcher modifies the test by inserting a set of very 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 α = .01.

given that 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 µ= 100 and a standard deviation of σ = 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions and gives the modified test to a sample of n = 36 students.

Set up hypotheses as

[tex]H_0: \bar x= 100\\H_a: \bar x >100[/tex]

(right tailed test at 1% level)

Mean difference = 104-100 =4

Std error of mean = [tex]\frac{\sigma}{\sqrt{n} } \\=3[/tex]

Since population std deviation is known and also sample size >30 we can use z statistic

Z statistic= mean diff/std error = 1.333

p value = 0.091266

since p >0.01, we accept null hypothesis.

There is no significant improvement in the scores because of inserting easy questions at 1% significance level