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Question:
The available options are:
(A) There is convincing evidence that there is no difference in the mean delivery times.
(B) There is convincing evidence that there is a difference in the mean delivery times.
(C) There is convincing evidence that the mean delivery time from Japan to Texas is greater than the mean delivery time from Texas to Japan.
(D) There is not convincing evidence that the mean delivery time from Japan to Texas is greater than the mean delivery time from Texas to Japan. (E) The t-test cannot be used for sample sizes that are this small.
Answer:
The correct option is;
(A) There is convincing evidence that there is no difference in the mean delivery times.
Step-by-step explanation:
Here we have the formula for the two-sample t-test given s;
To Texas N₁ = 12, =8.74 σ₁ = 2.92 SE Mean₁ = 0.84
To Japan N₂ = 9 = 6.75 σ₂ = 2.56 SE Mean₁ = 0.85
t = 1.667
Where the null hypothesis is
mu To Texas = mu To Japan and the alternative is
mu To Texas > mu To Japan
Here since the observed P value of P = 0.058 is greater than the significance level of 0.05 we fail to reject the null hypothesis and we will therefore, not accept the alternative hypothesis.
Hence, there is convincing evidence that there is no difference in the mean delivery times.