File: Ch16, Chapter 16: ChiSquare Analysis
True/False
1. In a chisquare goodnessoffit test, theoretical frequencies are also called expected frequencies.
Ans: True
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Easy
2. In a chisquare goodnessoffit test, actual frequencies are also called calculated frequencies.
Ans: False
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Easy
3. The number of degrees of freedom in a chisquare goodnessoffit test is the number of categories minus the number of parameters estimated.
Ans: False
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Easy
4. The number of degrees of freedom in a chisquare goodnessoffit test is the number of categories minus the number of parameters estimated minus one.
Ans: True
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Easy
5. A chisquare goodnessoffit test is being used to test the goodnessoffit of a normal distribution (the mean and the standard deviation of which must be estimated) for a data with "k" categories. This test has (k3) degrees of freedom.
Ans: True
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
6. The null hypothesis in a chisquare goodnessoffit test is that the observed distribution is the same as the expected distribution.
Ans: True
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
7. The decision rule in a chisquare goodnessoffit test is to reject the null hypothesis if the computed chisquare is greater than the table chisquare.
Ans: True
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
8. When using the chisquare goodnessoffit test, we must make sure that none of the expected frequencies is less than 30.
Ans: False
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
9. A chisquare goodnessoffit test to determine if the observed frequencies in seven categories are uniformly distributed has six degrees of freedom.
Ans: True
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
10. A chisquare goodnessoffit test to determine if the observed frequencies in ten categories are Poisson distributed has nine degrees of freedom.
Ans: False
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
11. A twoway table used for a test of independence is sometimes called a contingency table.
Ans: True
Response: See section 16.2 Contingency Analysis: ChiSquare Test of Independence
Difficulty: Easy
12. In a chisquare test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 12.
Ans: False
Response: See section 16.2 Contingency Analysis: ChiSquare Test of Independence
Difficulty: Easy
13. In a chisquare test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 7.
Ans: False
Response: See section 16.2 Contingency Analysis: ChiSquare Test of Independence
Difficulty: Easy
14. In a chisquare test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 6.
Ans: True
Response: See section 16.2 Contingency Analysis: ChiSquare Test of Independence
Difficulty: Easy
15. The null hypothesis for a chisquare test of independence is that the two variables are not related.
Ans: True
Response: See section 16.2 Contingency Analysis: ChiSquare Test of Independence
Difficulty: Easy
Multiple Choice
16. A goodness of fit test is to be performed to see if consumers prefer any of three package designs (A, B, and C) more than the other two. A sample of 60 consumers is used. What is the expected frequency for category A?
a) 1/3
b) 20
c) 60
d) 10
e) 30
Ans: b
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Easy
17. A goodness of fit test is to be performed to see if Web Surfers prefer any of four Web sites (A, B, C and D) more than the other three. A sample of 60 consumers is used. What is the expected frequency for Web site A?
a) 1/4
b) 20
c) 15
d) 10
e) 30
Ans: c
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Easy
18. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using a = .01, the degrees of freedom for this test are _______.
a) 5
b) 4
c) 3
d) 2
e) 1
Ans: b
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
19. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using a = .01, the critical value of chisquare is _______.
a) 7.78
b) 15.09
c) 9.24
d) 13.28
e) 15.48
Ans: d
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
20. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using a = .01, the observed value of chisquare is _______.
a) 12.09
b) 9.82
c) 13.28
d) 17.81
e) 2.09
Ans: e
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Middle
21. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using a = .01, the appropriate decision is _______.
a) reject the null hypothesis that the observed distribution is uniform
b) reject the null hypothesis that the observed distribution is not uniform
c) do not reject the null hypothesis that the observed distribution is uniform
d) do not reject the null hypothesis that the observed distribution is not uniform
e) do nothing
Ans: c
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Hard
22. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26. Using a = .01, the critical chisquare value is _______.
a) 13.277
b) 15.086
c) 7.779
d) 11.070
e) 14.356
Ans: a
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
23. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26. Using a = .01, the observed chisquare value is _______.
a) 1.18
b) 9.10
c) 20.27
d) 4.51
e) 19.70
Ans: b
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
24. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26. Using a = .01, the appropriate decision is _______.
a) do not reject the null hypothesis that the observed distribution is uniform
b) do not reject the null hypothesis that the observed distribution is not uniform
c) reject the null hypothesis that the observed distribution is uniform
d) reject the null hypothesis that the observed distribution is not uniform
e) do nothing
Ans: a
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Hard
25. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26. Using a = .10, the appropriate decision is _______.
a) do not reject the null hypothesis that the observed distribution is uniform
b) do not reject the null hypothesis that the observed distribution is not uniform
c) reject the null hypothesis that the observed distribution is uniform
d) reject the null hypothesis that the observed distribution is not uniform
e) do nothing
Ans: c
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Hard
26. A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using a = .05, the critical chiÂ square value is _______.
a) 13.277
b) 15.086
c) 7.8147
d) 11.070
e) 15.546
Ans: c
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Easy
27. A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using a = .05, the observed chisquare value is _______.
a) 5.418
b) 9.10
c) 20.27
d) 4.51
e) 7.86
Ans: a
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
28. A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using a = .05, the appropriate decision is _______.
a) do not reject the null hypothesis that the observed distribution is uniform
b) do not reject the null hypothesis that the observed distribution is not uniform
c) reject the null hypothesis that the observed distribution is uniform
d) reject the null hypothesis that the observed distribution is not uniform
e) do nothing
Ans: a
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Hard
29. A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using a = .10, the appropriate decision is _______.
a) do not reject the null hypothesis that the observed distribution is uniform
b) do not reject the null hypothesis that the observed distribution is not uniform
c) reject the null hypothesis that the observed distribution is uniform
d) reject the null hypothesis that the observed distribution is not uniform
e) do nothing
Ans: a
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Hard
30. A chisquare goodness of fit test is to be performed to see if data fit the Poisson distribution. There are 6 categories, and lambda must be estimated. How many degrees of freedom should be used?
a) 6
b) 5
c) 4
d) 3
e) 2
Ans: c
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
31. A chisquare goodness of fit test is to be performed to see if data fit the Poisson distribution. There are 8 categories, and lambda must be estimated. How many degrees of freedom should be used?
a) 8
b) 7
c) 6
d) 5
e) 4
Ans: c
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
32. A chisquare goodness of fit test is to be performed to see if data fit the Poisson distribution. There are 8 categories, and lambda must be estimated. Alpha is chosen to be 0.10. The critical (table) value of chisquare is _______.
a) 10.645
b) 12.017
c) 3.828
d) 16.812
e) 17.345
Ans: a
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Easy
33. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected:
Category

0

1

2

3

4

5

Observed

47

56

39

22

18

10

Using a = 0.10, the critical chisquare value for this goodnessoffit test is _______.
a) 1.064
b) 13.277
c) 9.236
d) 8.799
e) 7.779
Ans: e
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Easy
34. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected:
Category

0

1

2

3

4

5

Observed

47

56

39

22

18

10

Using a = 0.10, the observed chisquare value for this goodnessoffit test is ____.
a) 2.28
b) 14.56
c) 17.43
d) 1.68
e) 2.67
Ans: b
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Hard
35. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected:
Category

0

1

2

3

4

>5

Observed

7

18

25

17

12

5

Using a = 0.10, the critical value of chisquare for the data is _______.
a) 9.236
b) 7.779
b) 1.064
c) 13.277
d) 12.89
Ans: b
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
36. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected:
Category

0

1

2

3

4

>5

Observed

7

18

25

17

12

5

Using a = 0.10, the value of the observed chisquare for the data is _______.
a) 19.37
b) 2.29
c) 1.74
d) 3.28
e) 4.48
Ans: c
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Hard
37. Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis.
Cars per 15 minute interval

0

1

2

3

4

>5

Observed Frequency

5

15

17

12

10

8

The number of degrees of freedom for this goodnessoffit test is _______.
a) 5
b) 4
c) 3
d) 2
e) 1
Ans: b
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
38. Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis.
Cars per 15 minute interval

0

1

2

3

4

>5

Observed Frequency

5

15

17

12

10

8

Using a = 0.05, the critical value of chisquare for this goodnessoffit test is ____.
a) 9.49
b) 7.81
c) 7.78
d) 11.07
e) 12.77
Ans: a
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Medium
39. Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis.
Cars per 15 minute interval

0

1

2

3

4

>5

Observed Frequency

5

15

17

12

10

8

The observed value of chisquare for this goodnessoffit test is _____.
a) 0.73
b) 6.72
c) 3.15
d) 7.81
e) 9.87
Ans: a
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Hard
40. Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis.
Cars per 15 minute interval

0

1

2

3

4

>5

Observed Frequency

5

15

17

12

10

8

Using a = 0.05, the appropriate decision for this goodnessoffit test is ____.
a) reject the null hypothesis that the observed distribution is Poisson
b) reject the null hypothesis that the observed distribution is not Poisson
c) do not reject the null hypothesis that the observed distribution is not Poisson
d) do not reject the null hypothesis that the observed distribution is Poisson
e) do nothing
Ans: d
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Hard
41. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is: "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Ophelia's null hypothesis is _______.
a) p > 0.05
b) p = 0.05
c) m 30
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