Multiple Choice. For each of the following clearly place the one letter to the most correct answer in the blank provided. ( 8 points each )

 

___________  1. )       30 people are randomly selected from a certain town and their

mean age is 85.1.  Find a 95 percent confidence interval for the true mean age of everyone in the town is the population standard deviation is 4.5.

 

a.  )      ( 84.05, 86.15 )           

b.  )      ( 83.50, 86.70 )

c.  )      ( 82.93, 87.27 )           

d.  )      ( 83.49, 86.71 )

 

 

 

 

 

 

___________  2. )       The owner of a football team claims that the average

attendance at games is over 60,100, and he is therefore justified in moving the team to a city with a larger stadium.  Identify the type II error for the test.

 

a. )       The error of rejecting the claim that the mean attendance is at most 60,100, when it really is at most 60,100.

b. )       The error of failing to reject the claim that the mean attendance is at most 60,100, when it is actually greater than 60,100.

c. )       The error of failing to reject the claim that the mean attendance is more than 60,100, when it is actually less than 60,100.

 

___________  3. )       Use the given degree of confidence and sample data to

construct a 98 percent confidence interval for the population proportion, p :  n = 86,  x = 34. 

 

a.  )      ( 0.273, 0.518 )           

b.  )      ( 0.291, 0.499 )

c.  )      ( 0.271, 0.519 )           

d.  )      ( 0.292, 0.498 )

 

 

 

 

 

 

_________   4. )         A researcher wants to check the claim that convicted burglars

spend an average of 18.7 months in jail.  She takes a random sample of 67 such cases from court files and finds the mean is 16.8 months.  Find the p-value for the test of the claim that  if the population standard deviation is 7.3 months.

 

a. )       0.0332

b. )       0.4834

c. )       -0.0166

d. )       0.0166

 

 

 

 

 

 

 

 

 

___________  5. )       If the p-value for a test statistic is 0.018 and the significance

level is 0.05 then the appropriate decision is :

 

a. )       Reject H0

b. )       Accept H0

c. )       Reject Ha

d. )       Fail to Reject H0

 

 

___________  6. )       Compute the test statistic used to test the alternative

hypothesis :  if , ,  and .

 

a. )       -0.670

b. )       -0.001

c. )       -0.158

d. )       -0.394

 

 

 

 

 

 

 

 

 

 

 

 

7. )       Ten observations are drawn from each of two independent populations with

the following sample statistics :   and  .  Test the claim that the variances are not equal at  significance level.  There should be 6 steps to the hypothesis test.     ( 16 points )

 

 

 

 

8. )       A coach uses a new technique in training middle distance runners.  The times

for 8 different athletes to run 800 meters before and after this training are shown below.

 

Athlete                        A            B        C         D         E          F          G         H

 

Before

Training          115.2   120.9   108.0   112.4   107.5   119.1   121.3   122.3  

After

Training          116.0   119.1   105.1   111.9   109.1   115.2   118.5   120.9

 

Test the claim that there is a decrease in time after training at  significance level. There should be 6 steps to the hypothesis test.  ( 18 points )

 

 

 

9. )       The Better Cookie Company claims its chocolate chip cookies have more

chips than another chocolate chip cookie.  120 Better cookies and 100 of the other type of cookie were randomly selected and the number of chips in each cookie was recorded.  The results are as follows :

                                                Better             Another

Mean number of chips             7.6                    6.9

            Standard deviation                   1.4                    1.7

 

Test the claim that the population of Better Cookies has a higher mean number of chips at  level of significance.  There should be 6 steps to the hypothesis test.    ( 18 points  )