1. A salesperson claims that at least 40% of the people that come into the store make a purchase. To test this claim, the store manager selected a sample of 100 people in the store and found that 37 made a purchase. State the p-value for the test accurate to 4 decimal places.
2. Suppose that a random sample of 100 observations from a population gives a value p ^ =.68 and you wish to test the null hypothesis that p = .75 against the alternate hypothesis that p<.75 Find the p-value for the test correct to 3 decimal places.
3. A college professor feels that students are doing better in a certain statistics class than usual. Normally, the college has a 52% passing rate in that particular course. In a sample of 54 students, it was found that 32 passed. Conduct a test of hypothesis and give the p-value correct to 4 decimal places.