Question

A researcher would like to test whether a new teaching method enhances the concept understanding. In a paired sample t test, a random sample of 20 students were given a pre-test before a new method was introduced. After the new method was introduced , a post test was given. The differences of pre-test scores and post test scores ( d = post test score - pre test score) were recorded for all students. The sample mean difference and the standard deviation of differences for the 20 students were 2.82 and 3.7 respectively. What is the value of the t test statistic (for two decimal places) for the paired sample test?

Answer 1

To calculate the t-test statistic for a paired sample t-test, we can use the formula: t = (mean difference - hypothesized mean difference) / (standard deviation of the differences / sqrt(sample size)). However, the question does not provide a hypothesized mean difference, so the exact t-test statistic cannot be calculated.

Step-by-step explanation:

To calculate the t-test statistic for a paired sample t-test, we can use the formula:

t = (mean difference - hypothesized mean difference) / (standard deviation of the differences / sqrt(sample size))

In this case, the mean difference is 2.82, the standard deviation of the differences is 3.7, and the sample size is 20. Let's plug in these values:

t = (2.82 - hypothesized mean difference) / (3.7 / sqrt(20))

Since the question does not provide a hypothesized mean difference, we can't calculate the exact t-test statistic. The value of the t-test statistic will depend on the hypothesized mean difference.

Answer 2

Answer: t= 3.41

Step-by-step explanation:

The t test statistic for the paired sample test is given by :-

`t=\frac{\overline{d}}{(s_d)/(√(n))}`

, where n = sample size.

`\overline{d}` = sample mean difference for n

`s_d` = sample standard deviation of differences for n.

Given : The sample mean difference and the standard deviation of differences for the 20 students were 2.82 and 3.7 respectively.

As per given , we have

n=20

`\overline{d}=2.82`

`s_d=3.7`

Then , the test statistic would be :-

`t=(2.82)/((3.7)/(√(20)))\\\\=(2.82)/(0.827345)=3.40849280895\approx3.41`

Hence, the value of the t test statistic for the paired sample test : t= 3.41