Using the t-distribution, it is found that since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.
At the null hypothesis, we <u>test if the groups have the same values</u>, that is, the subtraction of their means is 0:
At the alternative hypothesis, we <u>test if the groups have different values</u>, that is, the subtraction of their means is different of 0:
First, we have to find the mean and the standard deviation for both samples, hence, using a calculator:
The standard errors are:
For the distribution of differences, we have that:
We have the <u>standard deviation for the samples</u>, hence, the t-distribution is used. The test statistic is given by:
In which is the value tested at the null hypothesis, which is 0 for this problem. Hence, the value of the test statistic is:
To find the p-value, we have a <u>two-tailed test</u>, as we test if the means are different from a value, with <u>t = 0.37</u> and 8 + 8 - 2 = <u>14 df</u>.
Using a t-distribution calculator, this p-value is of 0.72.
Since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.
A similar problem is given at brainly.com/question/15682365