A control group of 8 students were given the same test twice to see whether reta
ID: 3149911 • Letter: A
Question
A control group of 8 students were given the same test twice to see whether retaking the test affected the score. Below are their scores on their first and second attempts. Test the claim that the differences have a mean of zero using a 0.05 significance level. What do the results suggest? Can the null hypothesis be rejected? Yes, because the test statistic does not fall in the critical region. No, because the test statistic falls in the critical region. Yes, because the test statistic falls in the critical region., No, because the test statistic does not fall in the critical region. This suggests that it that the scores are the same after retesting.Explanation / Answer
Let ud = u2 - u1.
The differences are
30
70
40
10
30
40
70
70
Formulating the null and alternative hypotheses,
Ho: ud = 0
Ha: ud =/ 0
At level of significance = 0.05
As we can see, this is a two tailed test.
Calculating the standard deviation of the differences (third column):
s = 28.60387768
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 10.11299794
Calculating the mean of the differences (third column):
XD = 45
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = 4.449719092
As df = n - 1 = 7
Then the critical value of t is
tcrit = +/- 2.364624252
As |t| > 2.635, WE REJECT THE NULL HYPOTHESIS.
Hence,
OPTION C: Yes, because the test statistic falls in the critical region. [ANSWER]
******************************************************
Hence, the score are NOT THE SAME after retesting.
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