Questions for Modules 4-5

 

Note: you should try these questions after you have read and understood modules 4-5 and chapters 7-12.


Note: draw the curve and label if this was a real test. You would also want to show all of your work.

  1. A toothpaste manufacturer wants to determine whether the addition of a certain chemical to his toothpaste will increase its ability to fight tooth decay. Two groups of 100 people each are chosen and an experiment is conducted. Of the 100 people using the toothpaste with the chemical addition for a specified period of time, the manufacturer finds that they have an average of 8 cavities standard deviation of 3 cavities.  The average number of cavities of the 100 people using the toothpaste without the chemical addition is 9 with a standard deviation of 4.

 

  1. Can we conclude at the 1% level of significance (a=.01) that the addition of the chemical increased the toothpaste’s ability to fight tooth decay?
  2. State Ho and Ha (what do we accept or reject)

 Answer 1


2.  In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated.

Company A:

N1=80

x1=$6.75

S1=$1

Company B:

N2=60

x2=$6.25

S2=$0.95

 

a.  Is there any significant difference between the hourly wages of the two companies?

 b.  State Ho and Ha (what do we accept or reject). Level of significance is .05

  Answer 2

 


  1. A reading test is given to an elementary school class that consists of 12 Anglo-American children and 10 Mexican-American children. The results of the test are:

 

x1 for AA children 74, S1=8; MM Children, x2=70, S2=10 (assume normal distribution). 

    1. Is the difference between the means of the two groups significant at the .05 (a=.05) level of significance?
    2. State Ho and Ha (what do we accept or reject). Level of significance is .05.(a=.05)

  Answer 3


4. Two of the major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two models of cars. A random sample of 8 cars from each manufacturer is selected, and 8 drivers are selected to drive each automobile for a specified distance. The following data show the results of the test.

   

Driver               Model A (MPG)      Model B (MPG)

1                                29                       27

2                                24                       23

3                                26                       28

4                                24                       23

5                                25                       24

6                                27                       26

7                                30                       28

8                                25                       27

 

Test at (a=.05) to determine if there is a difference in the average MPG of the two models.

  1. What is Ho Ha, what do you reject?
  2. One or two tailed test
  3. Your conclusion

  Answer 4


5. A large corporation wants to determine whether or not a “typing efficiency” course given at a local college can increase the typing speed of their secretaries. A sample of 6 secretaries is selected, and they are sent to take the course. The typing speeds of the secretaries in words per minute (WPM) are shown below:

 

Secretary          Before the course (WPM)           After the course (WPM)

1                                65                                                  68

2                                60                                                  62

3                                61                                                  66

4                                63                                                  66

5                                64                                                  67

6                                65                                                  67

 

Use (a=.05) and test to see if it can be concluded that taking the course will actually increase the average typing speeds of the secretaries.

 

a. What is Ho Ha, what do you reject?

b. One or two tailed test

c. Your conclusion

 

 Answer 5


  1. A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is adverting that their new tires’ life expectancy has increased. In order to test the legitimacy of their advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data:

  Life Expectancy (in thousands of miles)
28,27,25,28,29,25

 

Use (a=.01) and test to determine whether or not the tire company is using legitimate advertising.

 

  1. What is Ho Ha, what do you reject?
  2. Your conclusion?

  What is the 90% confidence interval for the population mean?

 

 Answer 6


  1. Cranston, Rhode Island has the reputation for selling the most expensive bubble gum in the U.S. Ten candy stores were surveyed and it was found that the average price in the 10 stores was 4 cents (.04 dollars) with a standard deviation of half a penny (.005 dollars or s=.005). Find 95% confidence interval for m, the mean price of bubble gum in Cranston.

 Answer 7


8.   In a sample of 80 chief executive officers (CEO's) in Atlanta  only 12 of them had advanced degrees.. There are indications that nationally 16% of all CEO's had advanced college degrees. . Use a .05 LOS (a=.05) in order to determine whether or not the percentage of the  Atlanta CEO's who have advanced degrees is significantly less than the national average.

  1. What is Ho Ha, what do you reject?
  2. Your conclusion?

 

What is the 95% confidence interval for the population mean?

 Answer 8


9. Last school year, the student body of a local college consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year’s student body showed the following number of students in each classification:

 

Freshmen 83

Sophomores 68

Juniors 85

Seniors 64

Total=300

 

Has there been any significant change in the number of students in each classification between the last school year and this school year? Use a LOS=.05

  1. What is Ho Ha, what do you reject?

b.  Your conclusion?

 

 Answer 9


10.  A group of 500 individuals were asked to cast their votes regarding a particular issue in the Equal Rights Amendment. The following contingency table shows the results of the votes:

 
Sex       Undecided     Favor      Oppose     Total
Female    180        80                    40            300
Male         150        20                    30            200
Total          330       100                  70             500

Test LOS=0.05 (a=.05) to determine if the votes cast were independent of the sex of the individuals.

 

a.  What is Ho Ha, what do you reject?

  1. Your conclusion?

Answer 10


11.  Suppose that you wish to investigate whether there really is a relationship between an employee's performance in a company training program and the employee's ultimate success on the job.  You take a random sample of 200 cases from the company's extensive files of employees who completed the program.  The results are as follows: 

 
Success on Job

                          Performance in Training Program                 

   
 

Below Average

Average

Above Average

Poor

30

15

 5

Average

10

70

20

Very Good

8

15

27

Analyze your data using a 0.01 (a=.01) level of significance.

     Answer 11