Question 6.14: A pollster will conduct a survey of a random sample of voter...
A pollster will conduct a survey of a random sample of voters in a community to estimate the proportion who suppo1t a measure on school bonds. Let p be the proportion of the population who support the measure. The pollster will test H_0: p = 0.50 versus H_1: p ≠ 0.50 at the 5% level. If 200 voters are sampled, what is the power of the test if the true value of p is 0.55?
The following computer output (from MINITAB) presents the solution:
Power and Sample Size
Test for One Proportion
Testing proportion = 0.5 (versus not = 0.5)
Alpha = 0.05
Alternative Sample
Proportion Size Power
0.55 200 0.292022
The first two lines of output state that this is a power calculation for a test for a single population proportion p. The next two lines state the null and alternate hypotheses, and the significance level of the test. Note that we have specified a two-tailed test with significance level α = 0.05. Next is the alternative proportion, which is the value of p (0.55) that we are assuming to be true when the power is calculated. The sample size has been specified to be 200, and the power is computed to be 0.292.