Question

A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of n=1100 registered voters and found that 570 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state who would vote for the Republican candidate. We test H0:p=.50 Ha:p>.50 (a) What is the z-statistic for this test? (b) What is the P-value of the test?

Answer 1

Part A

p = 0.5 is the hypothesized population proportion

x = 570 is the number of successes

n = 1100 is the sample size

phat = x/n = 570/1100 = 0.518182 is the approximate sample proportion

SE = standard error

SE = sqrt(p*(1-p)/n)

SE = sqrt(0.5*(1-0.5)/1100)

SE = 0.015076 which is approximate

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We have enough to compute the z test statistic

z = (phat - p)/(SE)

z = (0.518182 - 0.5)/(0.015076)

z = 1.206023

z = 1.21

Answer: The z-statistic is approximately 1.21

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Part B

Compute the probability of getting a z score larger than 1.21

P(Z > 1.21) = 1 - P(Z < 1.21)

P(Z > 1.21) = 1 - 0.8869 .... see note below

P(Z > 1.21) = 0.1131

note: the value 0.8869 comes from the table that I've attached as an image below. I have marked in red the proper row and column used to look up the value. The z table is commonly found in statistics textbooks toward the back sections. There are also many free online z tables you can search out as well. I used a z table found online. Alternatively, you can use your TI83 or TI84 calculator to compute the area under the normal curve. You would use the normalCDF function.

Answer: The P-value is approximately 0.1131