Question

1) Suppose n₁ = 15, n₂ = 12, the means for samples 1 and 2 are 70.5 and 78.5, respectively, and the standard deviations for samples 1 and 2 are 8.27 and 8.38, respectively. Test H₀: μ₁ ≤ μ₂ vs. H_a: μ₁ > μ₂ using α = 0.05. Be sure to:
a) Address all necessary assumptions for running a t-test;
b) Regardless of whether or not the assumptions are met, run a t-test. calculate the test statistic;
c) Calculate the p-value;
d) State your conclusion;
e) Construct and interpret a 95% confidence interval for the difference between the two population means.

2) A researcher investigated the effects of cold on hypertension in rats by randomly assigning six rats to a 26°C environment and six to a 5°C environment and recording their blood pressures.

Rat	1	2	3	4	5	6	7	8	9	10	11	12
Temp (°C)	26	26	26	26	26	26	5	5	5	5	5	5
Blood Pressure	152	149	176	157	182	179	369	354	423	366	375	384

a) Check the assumptions for running a t-test for the difference between the two treatment means. Which ones are satisfied and which aren’t Explain.
b) Regardless of your answer to part (a), run a t-test for the difference between the two treatment means at the α = 5% level of significance. Specifically, we are interested in knowing if there exists sufficient statistical evidence to support the claim that low temperatures increase blood pressure in rats. Be sure to state the null and alternative hypotheses, calculate the appropriate test statistic, calculate the p-value, and state your conclusions.
c) Construct a t-interval for the difference between the blood pressures of the two treatment groups. Use 95% confidence.

Answer 1