Question

A candidate for district attorney claims that 75% of all residents in Elko County, Nevada, favor granting police additional powers to tap telephone lines. In order to check this claim, a random sample of 560 residents was selected, and 392 said they were in favor of more phone taps.

a. Is there any evidence to suggest that the true proportion of residents who favor additional power to tap phones is less than 0.75? Use α = 0.01.

b. Compute the p-value associated with this hypothesis test.

Answer 1

H0: p = 0.75

Ha: p < 0.75

Sample proportion = 392 / 560 = 0.70

Test statistics

z = - p / sqrt( p (1 - p) / n)

= 0.70 - 0.75 / sqrt( 0.75 * 0.25 / 560)

= -2.73

This is test statistics value.

Critical value at 0.01 level is -2.326

Since test statistics < -2.326, we have sufficient evidence to reject H0.

We conclude at 0.01 level that we have enough evidence to support the claim.

b)

p-value = P( Z < z)

= P( Z < -2.73)

= 1 - P( Z < 2.73)

= 1 - 0.9968

= 0.0032