Question

colleague has told you she is interested in learning if using iPads as teaching tools will affect students’ performance on a practice standardized math test. She plans to have the students complete the practice test at the beginning and end of the third nine weeks. What type of hypothesis test would you recommend she perform? What would you tell her if she asked for a basic overview of the test and why she should use it?

Answer 1

Type of hypothesis test recommended to perform : Paired t-test;

A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample.

Before-and-after observations on the same subjects i.e. students’ practice standardized math test results at the beginning and end of the third nine weeks

basic overview of the test

Suppose a sample of n students were given a practice standardized math test at the beginning and end of the third nine weeks.We want to find out if, in general, if using iPads as teaching tools to improvements in students’ test scores. We can use the results from our sample of students to draw conclusions about the impact ofusing iPads as teaching tools .

Let x = test score before , y = test score after

To test the null hypothesis that the true mean difference is zero, the procedure is as follows:

1. Calculate the difference (di = yi − xi) between the two observations on each pair, making sure you distinguish between positive and negative differences.

2. Calculate the mean difference,

3. Calculate the standard deviation of the differences, s_d, and use this to calculate the standard error of the mean difference,

4. Calculate the t-statistic, which is given by

Under the null hypothesis, this statistic follows a t-distribution with n − 1 degrees of freedom.

5. Use tables of the t-distribution to compare value for t to the t_n-1 distribution. This will give the p-value for the paired t-test.