I.For Exercises 1 - 3 in Test I, perform each of the following steps.

a. State the hypotheses and identify the claim.

b. Find the critical value(s).

c. Compute the test value.

d. Make the decision.

e. Summarize the results.

1.Warming and Ice Melt

The average depth of the Hudson Bay is 305 feet. Climatologists were interested in seeing if the effects of warming and ice melt were affecting the water level. Fifty-five measurements over a period of weeks yielded a sample mean of 306.2 feet. The population variance is known to be 3.57. Can it be concluded at the 0.05 level of significance that the average depth has increased? Is there evidence of what caused this to happen? Source: World Almanac and Book of Facts 2010.

2.Credit Card Debt

It has been reported that the average credit card debt for college seniors at the college bookstore for a specific college is P163,100.00. The student senate at a large university feels that their seniors have a debt much less than this, so it conducts a study of 50 randomly selected seniors and finds that the average debt is P149,750.00, and the population standard deviation is P55,000.00. With a = 0.05, is the student senate correct?

3.Heights of 1-Year-Olds

The average 1-year-old (both genders) is 29 inches tall. A random sample of 30 1-year-olds in a large day care franchise resulted in the following heights. At a 0.05, can it be concluded that the average height differs from 29 inches? Assume = 2.61.

252532292829.534323228

3230263031.53027292827

3526.525.529.5323028.52933 29.5

II.Read and analyze the following problem.

Car Thefts

You recently received a job with a company that manufactures an automobile antitheft device. To conduct an advertising campaign for the product, you need to make a claim about the number of automobile thefts per year. Since the population of various cities in the United States varies, you decide to use rates per 10,000 people. (The rates are based on the number of people living in the cities.) Your boss said that last year the theft rate per 10,000 people was 44 vehicles. You want to see if it has changed. The following are rates per 10,000 people for 36 randomly selected locations in the United States.

554212562134733969239473245155266641671553569120787025621151736585633752016

Source: Based on information from the National Insurance Crime Bureau.

Using this information, answer these questions.

1.What hypotheses would you use?

2.Is the sample considered small or large?

3.What assumption must be met before the hypothesis test can be conducted?

4.Which probability distribution would you use?

5.Would you select a one- or two-tailed test? Why?

6.What critical value(s) would you use?

7.Conduct a hypothesis test. Use = 30.3.

8.What is your decision?

9.What is your conclusion?

10.Give a brief statement summarizing your conclusion.

11.If you lived in a city whose population was about 50,000, how many automobile thefts per year would you expect to occur?