For each problem #1-5:
1) state your hypotheses; 2) draw a graph showing the critical z-scores and the rejection region; 3) calculate z-obtained; 4) make a conclusion.
•The average monthly spending on gasoline in New York State is $85 per person. A random sample of 453 respondents living in Albany area revealed that they spend, on average, $83 on fuel each month, with a standard deviation of 20. Do Albany residents spend different amount of money on fuel compared to the NYS average? Use α=0.01.
•On a scale from 1 to 10, the mean approval of homosexual relations in the U.S. is 7.8. The mean approval of homosexual relations in a sample of 150 California residents is 8.3, with the standard deviation of 2.2. Are California residents more likely to approve homosexual relations than the adults in the U.S.? Use α=0.05.
•Are single childless women more likely to receive messages on a dating site? On average, women receive 12 messages during their first week on a dating website. The analysis of a random sample of women without children (N = 72) taken from a dating website database show that they, on average, received 15 messages during their first week after the registration, with a standard deviation of 4.3. Use α = 0.05.
•Does college experience depend on one’s major? The mean satisfaction with college experience in a random sample of 48 math majors is 8.3 with a standard deviation of 2. The mean satisfaction with college experience of all students in the previous year is 7.8. Are math majors different from all other students in terms of their college satisfaction? Use α=0.01.
•To reduce the paperwork and administrative cost, a company wants to know whether employees are satisfied with the new reimbursement policy for meals during business travel. In an annual survey last year, 65% of all employees reported that they were satisfied with the old policy. To evaluate the new policy, the company conducts a new survey of 254 randomly selected employees, and finds that 160 of them support it. Is the new policy less popular than the old one? Use α = 0.05.