1. Answers to classwork on ch. 21

2. A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate using a random sample of 352 students and retained 18 students. Should the university continue its new programs? Test an appropriate hypothesis using α = 0.10 and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.
Not reject the null
There is not enough information to support the claim that the retention rate is greater then 4%.

3. The federal guideline for smog is 12% pollutants per 10,000 volume of air. A metropolitan city is trying to bring its smog level into federal guidelines. The city comes up with a new policy where city employees are to use city transportation to and from work. A local environmental group does not think the city is doing enough and no real decrease will occur. An independent agency hired by the city to run a test used a random sample size of 250 and found 38 units volumes polluted. Should the city continue its new policy? Test an appropriate hypothesis using α = 0.02 and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.
Not reject the null
There is not enough information to reject the claim that the cities smog rate is 12%.

4. A weight loss center provided a loss for 72% of its participants
A weight loss center provided a loss for 72% of its participants. The center's leader decides to test a new weight loss strategy on a random sample size of 140 and found 109 participants lost weight. Should the center continue its new strategy? Test an appropriate hypothesis using α = 0.02 and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.
Not reject the null
There is not enough information to support the claim that the weight loss rate is greater then 72%

5. A state survey investigates whether the proportion of 8% for employees who commute by car to work is higher than it was five years ago. A test on employee commuting by car was done on a random sample size of 1000 and found 120 commuters by car. Test an appropriate hypothesis using α = 0.01 and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.
Reject the null
There is enough information to support the claim that the proportion of employees that commute is greater then 8%

6. The U.S. Department of Labor and Statistics released the current unemployment rate of 5.3% for the month in the U.S. and claims the unemployment has not changed in the last two months. However, the states statistics reveal that there is a decrease in the U.S. unemployment rate. A test on unemployment was done on a random sample size of 1000 and found 38 people were unemployed. Should the state continue with its assumption of no change? Test an appropriate hypothesis using α = 0.05 and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.
Reject the null
There is enough information to reject the claim that the unemployment rate is still 5.3%

7. The city management company claims that 75% of all low income housing is 1500 sq. ft. The tenants believe the proportion of housing this size is smaller than the claim, and hire an independent engineering firm to test a random sample size of 120 and found 79 houses were smaller than 1500 sq. ft. Should the city continue with its assumption of 75%? Test an appropriate hypothesis using α = 0.05 and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.
Reject the null
There is enough information to reject the claim that 75% of all low income housing is 1500 sq. ft.