Answer:
There is no price difference between the two stores.
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.
In this case a paired t-test is used to determine if there is a price difference between the two stores.
The hypothesis for the test can be defined as follows:
H₀: There is no price difference between the two stores, i.e. d = 0.
Hₐ: There is a price difference between the two stores, i.e. d ≠ 0.
From the information provided the sample mean and standard deviation are:
[tex]\bar d=-0.464\\\\S_{d}=1.019[/tex]
Compute the test statistic value as follows:
[tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}=\frac{-0.464}{1.019/\sqrt{10}}=-1.4399\approx -1.44[/tex]
The test statistic value is -1.44.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
The degrees of freedom is:
n - 1 = 10 - 1 = 9
Compute the p-value of the test as follows:
[tex]p-value=2\cdot P(t_{\alpha/2, (n-1)}>-1.44)[/tex]
[tex]=2\cdot P(t_{0.10/2, 9}>-1.44)\\=2\times 0.092\\=0.184[/tex]
*Use a t-table.
The p-value of the test is 0.184.
p-value= 0.184 > α = 0.10
The null hypothesis was failed to be rejected.
Thus, it can be concluded that there is no price difference between the two stores.
