# Montarello and Martins (2005) found that fifth grade students completed more mathematics problems correctly when simple problems were mixed in with th

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 . 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 = 120, is this result sufficient to conclude that inserting the easy questions improves student performance? Use a one-tailed test with $\alpha =.05$.
The null hypothesis in words is ?
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Step 1
Solution:
Here $\mu =100,\sigma =24,n=36,\alpha =0.05,\stackrel{―}{x}=120$
${H}_{0}:\mu \le 100$
${H}_{1}:\mu \ge 100$
From Z Table,
z critical values = 1.96
Step 2
Test statistics
$z=\left(\stackrel{―}{x}-\mu \right)\frac{\sigma }{\sqrt{n}}=\frac{120-100}{24}/\sqrt{36}=5$
Since test statistics falls in rejection region, that is z > 1.96, we have sufficient evidence to reject ${H}_{0}$
We conclude at 0.05 level that Insering the easy questions improves student perfomance.