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 = 24. 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 α = .05.

The null hypothesis in words is Group of answer choices:

Inserting the easy questions decreases student performance on the achievement test

Inserting the easy questions does not affect student performance on the achievement test

Inserting the easy questions does not improve student performance on the achievement test

Inserting the easy questions improves student performance on the achievement test

The alternative hypothesis in symbols is

Group of answer choices

H1: µ ≤ 100

H1: µ > 100

H1: M ≤ 100

H1: M > 100

H1: µ = 100

H1: µ ≠ 100

The critical z value is

If it is a decimal number that is less than one, please include the 0 before the decimal point. If it is a decimal number with two or more than two places, leave only two decimal places after the decimal point. Please do not round. Finally, it is is a negative number, please do not forget to put the minus sign in front of it.

The z-score statistic is:

If it is a decimal number that is less than one, please include the 0 before the decimal point. If it is a decimal number with two or more than two places, leave only two decimal places after the decimal point. Please do not round. Finally, it is is a negative number, please do not forget to put the minus sign in front of it.

Your decision is

Group of answer choices

Reject the null hypothesis because the z-score statistic is greater than the critical z value

Reject the null hypothesis because the z-score statistic is not greater than the critical z value

Fail to reject the null hypothesis because the z-score statistic is greater than the critical z value

Fail to reject the null hypothesis because the z-score statistic is not greater than the critical z value

Answer 1

Here in this scenario it is given that the standardized mathematics achievement test that produces a normal distribution of scores with a mean of µ= 100 and a standard deviation of σ = 24.

Now researchers takes sample of size 36 and found that the sample mean is 120 . Now,

Claim : inserting the easy questions improves student performance.

To test the above claim we have to use one sample z test because here the population standard deviations is known.

Further the test is performed as below at 0.05 level of significance,

The null hypothesis in words is Group of answer choices:

Inserting the easy questions not improve the student performance on the achievement test.

Alternative hypothesis:

H1: µ > 100

Z critical value is 1.64.

Test Statistic value is 5.

Your decision is

Group of answer choices

Reject the null hypothesis because the z-score statistic is greater than the critical z value.

Hope it helps.

Thank you.