   Chapter 8, Problem 14P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Montarello and Martens (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.

To determine
If the average test score for the sample improves by inserting easy questions to the assignments. Use one tailed test with α=0.01.

Explanation

Given info:

The value of μ=100, M=104, σ=18, n=36 and α=0.01.

Calculation:

The null hypothesis (H0) states that there is no improvement in score of test by inserting easy questions.

Null hypothesis:

H0:μ100

Alternative hypothesis:

The alternative hypothesis states that there is improvement in the score of the test.

H1:μ>100

With α=0.01, the critical boundaries come out to be z=2.33 for one tailed test.

The distribution of sample follows normal distribution

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