In a survey of 5000 students taking the SAT, 350 were undecided on an intended college major. In another survey of 12,000 students taken 10 years before, 360 were undecided on an intended college major. At α = 0.10, can you reject the claim that the proportion of students taking the SAT who are undecided on an intended college major has not changed?

For each exercise, perform the steps below.

(a) Identify the claim and state H₀ and H_a.

(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test or a t-test. Explain your reasoning.

(c) Find the critical value(s) and identify the rejection region(s).

(d) Find the appropriate standardized test statistic.

(e) Decide whether to reject or fail to reject the null hypothesis.

(f) Interpret the decision in the context of the original claim.