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 H0: p = 0.50 versus H1: p ≠ 0.50 at the 5% level. If 200 voters

Question

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[latex]_0[/latex]: p = 0.50 versus H[latex]_1[/latex]: 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?

Accepted Answer

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.

Question 6.14: A pollster will conduct a survey of a random sample of voter...

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