Question

A political analyst was curious if younger adults were becoming more conservative. He decided to see if the mean age of registered Republicans was lower than that of registered Democrats. He selected an SRS of 128 registered Republicans from a list of registered Republicans and determined the mean age to be /X1 = = 39 years, with a standard deviation s₁ = 8 years. He also selected an independent SRS of 200 registered Democrats from a list of registered Democrats and determined the mean age to be /2 = 40 years, with a standard deviation s₂ = 10 years. Let μ1 and  μ2 represent the mean ages of the populations of all registered Republicans and Democrats, respectively. Suppose that the distributions of age in the populations of registered Republicans and of registered Democrats have the same standard deviation. Assume the pooled two-sample t procedures are safe to use.

Suppose the researcher had wished to test the hypotheses:

H₀: μ1= μ2, H_{a, :} μ1 < μμ2 .

The P-value for the pooled two-sample t test is:

a. larger than .10

b. between 0.05 and .10

c. between 0.01 and 0.05

d. below 0.01

Answer 1

Here using ti-83 calculator.

p-value = 0.1707

Answer : a) larger than 0.10

# Pooled standard deviation (Sxp)