Question

Consider the following hypothesis test:
H0: p = .20
Ha: p ? .20
A sample of 400 provided a sample proportion p-bar = .175.
a. Compute the value of the test statistic (to 2 decimals).
b. What is the p-value (to 4 decimals)?
2. Using a = .05, what is the critical value for the test statistic? (+ or -)

Answer 1

a. The test statistic is
Z=(pbar-p)/√[p*(1-p)/n]

=(0.175-0.2)/sqrt(0.2*0.8/400)

= -1.25

b. The p-value is 2*P(Z< -1.25)=0.2113 (check standard normal table)

Given a=0.05, the critical value is |Z(0.025)|=1.96 or -1.96 (check standard normal table)

Answer 2

a) test statistic is -1.25

b) p-value = 2*P(z < -1.25) = 2*.1056 = .2112

c) The critical values are +1.96 and -1.96