Answer:
1. E. Reject H0 if t > 1.721
2. B. 1.679
Step-by-step explanation:
This would be a hypothesis test for the difference between two means. In the way that the alternative hypothesis.
The critical value depends on the significance level, the test type (one-tail or two-tailed) and the degrees of freedom.
This is a t-test type, so the statistic is t and not z. In the way that the alternative hypothesis, where only matter if the mean A is significantly bigger than mean B, this is a one-tail test.
The degrees of freedom can be calculated as:
[tex]df=n_1+n_2-2=13+10-2=21[/tex]
Then, for a one-tail t-test, with significance level of 0.05 and 21 degrees of freedom, the critical value is t=1.721.
The standard deviation of the difference between the two means can be calculated as:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{5^2}{13}+\dfrac{3^2}{10}}\\\\\\s_{M_d}=\sqrt{1.923+0.9}=\sqrt{2.823}=1.6802[/tex]
