Data Analysis -Decision Making for Managers

1.

Suppose that a recent article stated that the mean time spent in jail by a first–time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years with a standard deviation of 1.8 years. Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.

2.

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. For each one of them, state the null hypothesis, H0, and the alternative hypothesis. Ha, in terms of the appropriate parameter (μ or p).

1. The mean number of years Americans work before retiring is 34.

2. At most 60% of Americans vote in presidential elections.

3. The mean starting salary for San Jose State University graduates is at least $100,000 per year.

4. Twenty-nine percent of high school seniors get drunk each month.

5. Fewer than 5% of adults ride the bus to work in Los Angeles.

6. The mean number of cars a person owns in her lifetime is not more than ten.

7. About half of Americans prefer to live away from cities, given the choice.

8. Europeans have a mean paid vacation each year of six weeks.

9. The chance of developing breast cancer is under 11% for women.

10. Private universities mean tuition cost is more than $20,000 per year.

3.

State the Type I and Type II errors in complete sentences given the following statements

1. The mean number of years Americans work before retiring is 34.

2. At most 60% of Americans vote in presidential elections.

3. The mean starting salary for San Jose State University graduates is at least $100,000 per year.

4. Twenty-nine percent of high school seniors get drunk each month.

5. Fewer than 5% of adults ride the bus to work in Los Angeles.

6. The mean number of cars a person owns in his or her lifetime is not more than ten.

7. About half of Americans prefer to live away from cities, given the choice.

8. Europeans have a mean paid vacation each year of six weeks.

9. The chance of developing breast cancer is under 11% for women.

10. Private universities mean tuition cost is more than $20,000 per year

4.

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.

1. Is this a test of one mean or proportion?

2. State the null and alternative hypotheses.

3. H0: ____________________ Ha: ____________________

4. Is this a right-tailed, left-tailed, or two-tailed test?

5. What symbol represents the random variable for this test?

6. In words, define the random variable for this test.

7. Calculate the following:

i. x = ________________

ii. n = ________________

iii. p′ = _____________

8. Calculate σx = __________. Show the formula set-up.

9. State the distribution to use for the hypothesis test.

10. Find the p-value.

11. At a pre-conceived α = 0.05, what is your:

i. Decision:

ii. Reason for the decision:

iii. Conclusion (write out in a complete sentence):

5.

For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college Statistics class to conduct a survey. The class randomly selected 100 patrons and found that 82 borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use α = 0.01 level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?