Question

A sample of 311 urban adult residents of a particular state revealed 61 who favored increasing the highway speed limit from 55 to 65 mph, whereas a sample of 171 rural residents yielded 70 who favored the increase. Does this data indicate that the sentiment for increasing the speed limit is different for the two groups of residents?

(a) Test H₀: p₁ − p₂ = 0 versus H_a: p₁ − p₂ ≠ 0 using α = 0.05, where p₁ refers to the urban population. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z =
P-value =

(b) If the true proportions favoring the increase are actually p₁ = 0.20 (urban) and p₂ = 0.42 (rural), what is the probability that H₀ will be rejected using a level 0.05 test with m = 311, n = 171? (Round your answer to four decimal places.)

Answer 1