Multiple step question?

Question

Suppose that during a one-half hour period 78 out of 128 cars at an intersection turned right. Perform the following steps to answer the question: "Is there sufficient evidence, at the 5% significance level, to say that more than 60% of the cars at this intersection turn right?"
a) What are the null and alternative hypotheses
b) What is the value of p ?
c) Is the sample size large enough for a z-test?
d) What is the value of the test-statistic?
e) What is the p-value?
f) If you are testing at the 5% significance level, is there enough evidence to say that the proportion of cars that turn right is more than 60%? Explain how you know

Answer 1

a) Ho = 60% turn right Ha = more than 60% turn right
This is a ONE-TAILED test on the far right extreme.

b) p = 78/128 = .609375 slightly more than .60 and approximately .61

c) yes, the sample size of 128 is significantly larger than the required 30 to do a z-test

d) test stat = (p - 60%)/sqrt(60%(1-60%)/128)
= (.61-.60)/sqrt(.6*.4/128) = 0.2309 approx. 0.23

e) p-value = P(z>0.23) = 0.4090

f)At a 5% significance level I fail to accept the Ho that more than 60% of the cars turn right. The reason I fail to accept is because the p-value (0.4090) is in excess of 5%.