Consider the following two questions designed to assess quantitative literacy.

1. What is 15% of 1000?
2. A store is offering a 15% off sale on all TVs. The most popular television is normally priced at $1000. How much money would a customer save on the television during this sale?

Suppose the first question is asked of 200 randomly selected college students, with166answering correctly; the second one is asked of a different random sample of 200 college students, resulting in141correct responses. Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context. (Usep₁for the true proportion students who answered the question without context correctly andp₂for the true proportion of students who answered the question with context correctly.)State the relevant hypotheses.

H₀:p₁p₂< 0 H_a:p₁p₂= 0H₀:p₁p₂= 0 H_a:p₁p₂> 0 H₀:p₁p₂= 0 H_a:p₁p₂0H₀:p₁p₂> 0 H_a:p₁p₂= 0H₀:p₁p₂= 0 H_a:p₁p₂< 0

Calculate the test statistic andP-value. (Round your test statistic to two decimal places and yourP-value to four decimal places.)z= P-value=