Question

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.

A)The alternative hypotheses in words is

B)The null hypothesis in symbols is

C)The critical z values is

D)The z-score statistic is:

E) Your decision is

Answer 1

Solution:

Given: 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.

We have to test if there is sufficient evidence to conclude that inserting the easy questions improves student performance.

Level of significance =

Sample Size = n = 36

Sample Mean = M= 104

Part A) The alternative hypotheses in words is:

Since we have to test if inserting the easy questions improves student performance,thus this is right tailed test.

thus

H1: inserting the easy questions improves student performance, that is :  µ > 100

In symbolic form:

Part B) The null hypothesis in symbols is

Part C) The critical z values is:

Given  Level of significance = and this is right tailed test,

thus find Area

Thus look in z table for Area = 0.9900 or its closest area and find corresponding z critical value.

Area 0.9901 is closest to 0.9900 , thus corresponding z value is 2.3 and 0.03

Thus z_critical = 2.33

Part D) The z-score statistic is:

Part E) Your decision is:

Decision rule: Reject null hypothesis H0, if z test statistic value > z critical value, otherwise we fail to reject H0.

Since z test statistic value = 1.33 < z critical value = 2.33, we fail to reject null hypothesis H0.

Thus this is result is not sufficient to conclude that inserting the easy questions improves student performance