The number of Wildland fires (in thousands) and wildland acres

Name: Test #4 (Chapter 10 and 7)

1. The number of Wildland fires (in thousands) and wildland acres burned (in millions) in the US for eight years is in the table below,

Fires (x)

84.1 73.5 63.6 65.5 66.8 96.4 85.7 79.0

Acres (y)

3.6 7.2 4.0 8.1 8.7 9.9 9.3 5.3

a. Calculate the sample correlation coefficient, r. Round to the nearest 1000th.

b. Describe the type of correlation coefficient and interpret the correlation in the context of the data.

2. The numbers of pass attempts and passing yards for seven professional quarterback for a recent year are listed in the table below. Round all answers to the nearest 1000th.

Pass attempts (x)

449 565 528 197 670 351 218

Passing Yards (y)

3265 4018 3669 1141 5177 2362 1737

a. Calculate the sample correlation coefficient, r.

b. Describe the type of correlation coefficient and interpret the correlation in the context of the data.

c. Test the significance of the correlation coefficient, r, that you found in part a. Use α=.05. Is there enough evidence to conclude that there is a significant linear relationship between the data?

d. Find the equation of the regression line for the data.

e. Use the regression equation to predict the average number passing yards if the pass attempts are 250.

3. Write each claim as a mathematical sentence. State the null and alternative hypotheses, identify which represents the claim, and state which whether the test would be a left-tailed test, a right-tailed test or a two-tailed test .

a. A school publicizes that the proportion of its students who earn scholarships to College is 85%

b. A grocery store says that the mean time wait in a line is less than 5 minutes.

c. A company advertises that the mean life of its furnaces is at least 15 years.

4. The P-value for a hypothesis test is P = 0.0321. What is your decision if the level of significance is:

a. α = 0.05?

b. α = 0.01

5. In auto racing, a pit crew claims that its mean pit stop time (for 4 new tires and fuel) is less than 13 seconds. A random selection of 32 pit stop times has a sample mean of 12.9 seconds. Assume the population standard deviation is 0.19 second. Is there enough evidence to support the claim at α = 0.01? Use a P-value.

6. An inventor has developed a new, energy efficient lawn mower engine. He claims that the engine will run continuously for 300 minutes on a single gallon of regular gasoline. From his stock of 2000 engines, the inventor selects a simple random sample of 50 engines for testing and finds the sample mean to be 295 minutes and sample standard deviation to be 20 minutes. Is there enough evidence to support his claim at the 5% level of significance? Assume the mean times are normally distributed.

1. A medical researcher says that less than 23% of US adults are smokers. In a random sample of 200 US adults, 19% say that they are smokers. At , is there enough evidence to support the researchers claim?α = . 05