Test the following pairs of hypotheses using the information given. Assume that the variable has been measured at the interval level and the cases have been selected at random. For each test, answer the following questions:

- Does the test require a one-tailed or a two-tailed test of statistical significance

- What is the value of the test statistics?

- What is the decision regarding the null hypothesis?

- Does the sample size suggest the need for caution in drawing conclusions?

a.

H₀ : 1 = 2

H₁ : 1 >2

= .01

x₁ = 50 x₂ = 35

s₁ = 40 s₂ = 25

N₁ = 514 N₂ = 430

b.

H₀ : 1 = 2

H₁ : 1 <2

= .05

x₁ = 3 x₂ = 5

s₁ = 1 s₂ = 2

N₁ = 87 N₂ = 34