Answer :
Answer:
Correct option is d. -1.
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
The hypothesis for the test can be defined as follows:
[tex]\text{H}_{0}:\mu_{d}=0\ \text{vs.}\ \text{H}_{\alpha}:\mu_{d}\neq0[/tex]
The test is given by:
[tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}[/tex]
Compute the differences as follows:
Individual Method 1 Method 2 Difference (d = 1 - 2)
1 7 5 2
2 5 9 -4
3 6 8 -2
4 7 7 0
5 5 6 -1
Compute the sample mean and sample standard deviation of the differences as follows:
[tex]\bar d=\frac{1}{n}\sum d=\frac{1}{5}\times [2-4-2+0-1]=-1\\\\S_{d}=\sqrt{\frac{1}{n-1}\sum (d-\bar d)^{2}}=\sqrt{\frac{1}{4}\times20}=2.2361[/tex]
Compute the test statistic as follows:
[tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}[/tex]
[tex]=\frac{-1}{2.2361/\sqrt{5}}\\\\=-1[/tex]
Thus, the test statistic for the difference between the two population means is -1.