A study conducted in September and October of 2010 found that fewer than half of employers who hired new college graduates last academic year plan to definitely do so again (The Wall Street Journal, November 29, 2010). Suppose the hiring intentions of the respondents were as follows:

Definitely hire Likely to hire Hire uncertain Will not hire
37% 17% 28% 18%

Six months later, a sample of 500 employers were asked their hiring intentions and gave the following responses:

Definitely hire Likely to hire Hire uncertain Will not hire
170 100 120 110

a. Choose the appropriate alternative hypothesis to test whether the proportions from the initial study have changed.
i. At least one of the population proportions differs from its hypothesized value.
ii. All population proportions differ from their hypothesized values.

b. Find the critical value at the 5% significance level.
c. Calculate the value of the test statistic.
d. What is the conclusion to the hypothesis test?

i. Reject H0; the proportions from the initial study have changed
ii. Reject H0; the proportions from the initial study have not changed
iii. Do not reject H0; the proportions from the initial study have changed
iv. Do not reject H0; the proportions from the initial study have not changed