Tutorial 6 Goodness of Fit and Contingency Table

Tutorial 6 Goodness of Fit and Contingency Table

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SUBJECT: Applied Statistics
CODE : BCT 2053 / -TUTORIAL 6-
CHAPTER 6

1. Students who are home-schooled often attend their local schools to participate in various types of activities such as sports or musicals ensembles. According to the government, 82% of home-scholars receive their education entirely at home, while 12% attend school up to 9 hours per week, and 6% spend from 9 to 25 hours per week at school. A survey of 85 students who are home-schooled revealed the following information about where there receive their education.

Entirely at home / Up to 9 hours / 9 to 25 hours
50 / 25 / 10

At α = 0.05, is there sufficient evidence to conclude that the proportions differ from those stated by the government?

2. A researcher whishes to see if the five ways (drinking decaffeinated beverages, taking a nap, going for a walk, eating a sugary snack, other) people use to combat midday drowsiness are equally distributed among office workers. A sample of 60 office workers is selected, and the following data are obtained.

Method / beverage / nap / walk / snack / other
Number / 21 / 16 / 10 / 8 / 5

At α = 0.01, can it be concluded that there is no preference?

3. Human blood type is grouped into four types (A, B, AB, O). The percentages of American with each type of blood area as follows: O, 43%; A, 40%; B, 12%; and AB, 5%. At a recent blood drive at a large university, the donors were classified as shown below.

O / A / B / AB
60 / 65 / 15 / 10

At α = 0.05, is there sufficient evidence to conclude that the proportions differ from those stated above?

4. A large supermarket carries four qualities of ground beef. Customers are believed to purchase these four varieties with probabilities of 0.10, 0.30. 0.35, and 0.25, respectively, from the least to most expensive. A sample of 500 purchases resulted in sales of 46, 162, 191, and 101 of the respected qualities. Does this sample contradict the expected proportions? Use α = 0.05.

5. A newspaper report that 21% of loans granted by credit unions were for home mortgages, 39% were for automobile purchases, 20% were for credit card and other unsecured loans, 12% were for real estate other than home loans, and 8% were for other miscellaneous needs. To see if her credit union customers had similar needs, a manager surveyed a random sample of 100 loans and found that 25 for home mortgages, 44 for automobile purchases, 19 for credit card and other unsecured loans, 8 for real estate other than home loans, and 4 for other miscellaneous needs. At α = 0.01, is the distribution the same as reported by the newspaper?

6. The data below shows the number of passes students for Statistics course according to their tutorial attendance.

Result
Pass / Fail
Attend tutorial / 50 / 8
Not attend tutorial / 28 / 14

Test a hypothesis that the result is not independent with tutorial attendance at significance level, α = 0.01.

7. A university official wishes to determine whether the instructor’s degree is related to the student’s opinion of the quality of instruction received. A sample of student’s evaluations of various instructors is selected and the data are shown below.

Rating / Degree
Bachelor’s / Master’s / Doctorate
Excellent / 14 / 9 / 4
Average / 16 / 5 / 7
Poor / 3 / 12 / 16

At α = 0.01, can the official conclude that the degree of the instructor is related to the students’ opinion about the instructor’s effectiveness in the classroom?

8. This table lists the number of officers and enlisted personnel for women in military.

Officers / Enlisted
Army / 10791 / 62491
Navy / 7816 / 42750
Marine Corps / 932 / 9525
Air Force / 11819 / 54344

At α = 0.05, is there a sufficient evidence to conclude that a relationship exist between rank and branch of the Armed Forces?

9. The vice president of a large supermarket chain whished to determine if his customers made a list before going grocery shopping. He surveyed 288 customers in three stores. The results are shown here.

Rating / Store
A / B / C
Made List / 77 / 74 / 68
No list / 19 / 22 / 28

At α = 0.01, test the claim that the proportions of the customers in the three stores who made a list before going shopping are equal.

10. A researcher whishes to see if the proportions of workers for each type of job have changed during the last 10 years. A sample of 100 workers is selected and the results are shown below.

services / manufacturing / government / other
10 years ago / 33 / 13 / 11 / 3
Now / 18 / 12 / 8 / 2

At α = 0.05, test the claim that the proportions have not changed.

ANSWERS

1. 82% of home-schoolers receive their education entirely at home, while 12% attend school up to 9 hours per week, and 6% spend from 9 to 25 hours per week at school , ,

2. There is no preference in the way people use to combat midday drowsiness, ,

3. The percentages of American with each type of blood area as follows: O, 43%; A, 40%; B, 12%; and AB, 5% , ,

4. Customers purchase these four varieties of ground beef with probabilities of 0.10, 0.30. 0.35, and 0.25, ,

6. The result is independent with tutorial attendance,,

7. The degree of the instructor is not related to the students’ opinion about the instructor’s effectiveness in the classroom, ,

8. There is no relationship exist between rank and branch of the Armed Forces, ,

9. The proportions of the customers in the three stores who made a list before going shopping are equal, ,

10. the proportions of workers for each type of job have not changed during the last 10 years, ,