# Statistics MCQs – Tests For Qualitative Data Part 1

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1. A chi-square test of association has 10 degrees of freedom. If the test statistic value is 26.56, then what is the most accurate statement that can be made about the p-value for the test?

a. p-value < 0.005

b. 0.005 < p-value < 0.01

c. 0.01 < p-value < 0.025

d. 0.025 < p-value < 0.05

e. 0.05 < p-value < 0.1

Answer: A

2. A chi-square test of association has 10 degrees of freedom. If the test statistic value is 24.04, then what is the most accurate statement that can be made about the p-value for the test?

a. p-value < 0.005

b. 0.005 < p-value < 0.01

c. 0.01 < p-value < 0.025

d. 0.025 < p-value < 0.05

e. 0.05 < p-value < 0.1

Answer: B

3. A chi-square test of association has 10 degrees of freedom. If the test statistic value is 22.48, then what is the most accurate statement that can be made about the p-value for the test?

a. p-value < 0.005

b. 0.005 < p-value < 0.01

c. 0.01 < p-value < 0.025

d. 0.025 < p-value < 0.05

e. 0.05 < p-value < 0.1

Answer: C

4. A chi-square test of association has 10 degrees of freedom. If the test statistic value is 19.35, then what is the most accurate statement that can be made about the p-value for the test?

a. p-value < 0.005

b. 0.005 < p-value < 0.01

c. 0.01 < p-value < 0.025

d. 0.025 < p-value < 0.05

e. 0.05 < p-value < 0.1

Answer: D

5. A chi-square test of association has 10 degrees of freedom. If the test statistic value is 17.24, then what is the most accurate statement that can be made about the p-value for the test?

a. p-value < 0.005

b. 0.005 < p-value < 0.01

c. 0.01 < p-value < 0.025

d. 0.025 < p-value < 0.05

e. 0.05 < p-value < 0.1

Answer: E

6. For a chi-squared random variable with 21 degrees of freedom and a significance level of 0.05, the value from the tables is 32.6705. Which of the following test statistic values would lead us to reject the null hypothesis in a test of association between two variables?

a. 23.45

b. 16.87

c. 41.56

d. 31.09

e. 29.44

Answer: C

7. For a chi-squared random variable with 21 degrees of freedom and a significance level of 0.05, the value from the tables is 32.6705. Which of the following test statistic values would lead us to not reject the null hypothesis in a test of association between two variables?

a. 43.45

b. 36.87

c. 41.56

d. 51.09

e. 29.44

Answer: E

8. In order to test whether a dice is unbiased it is rolled 100 times and the number of 1’s, 2’s, 3’s, 4’s, 5’s and 6’s rolled is recorded each time. Using a 5% significance level, the critical value from the table for the appropriate hypothesis test is:

a. 11.0705

b. 1.1455

c. 12.8325

d. 0.8612

e. 15.0863

Answer: A

9. In order to test whether a dice is unbiased it is rolled 100 times and the number of 1’s, 2’s, 3’s, 4’s, 5’s and 6’s rolled is recorded each time. Using a 2.5% significance level, the critical value from the table for the appropriate hypothesis test is:

a. 11.0705

b. 1.1455

c. 12.8325

d. 0.8612

e. 15.0863

Answer: C

10. In order to test whether a dice is unbiased it is rolled 100 times and the number of 1’s, 2’s, 3’s, 4’s, 5’s and 6’s rolled is recorded each time. Using a 1% significance level, the critical value from the table for the appropriate hypothesis test is:

a. 11.0705

b. 1.1455

c. 12.8325

d. 0.8612

e. 15.0863

Answer: E

11. A test for association between two variables is conducted using a contingency table. The table has 2 rows and 6 columns. What is the critical value from the table if the test is conducted at the 5% level of significance?

a. 11.0705

b. 12.5916

c. 14.0671

d. 15.5073

e. 16.9190

Answer: A

12. A test for association between two variables is conducted using a contingency table. The table has 3 rows and 4 columns. What is the critical value from the table if the test is conducted at the 5% level of significance?

a. 11.0705

b. 12.5916

c. 14.0671

d. 15.5073

e. 16.9190

Answer: B

13. A test for association between two variables is conducted using a contingency table. The table has 2 rows and 8 columns. What is the critical value from the table if the test is conducted at the 5% level of significance?

a. 11.0705

b. 12.5916

c. 14.0671

d. 15.5073

e. 16.9190

Answer: C

14. A test for association between two variables is conducted using a contingency table. The table has 3 rows and 5 columns. What is the critical value from the table if the test is conducted at the 5% level of significance?

a. 11.0705

b. 12.5916

c. 14.0671

d. 15.5073

e. 16.9190

Answer: D

15. A test for association between two variables is conducted using a contingency table. The table has 2 rows and 10 columns. What is the critical value from the table if the test is conducted at the 5% level of significance?

a. 11.0705

b. 12.5916

c. 14.0671

d. 15.5073

e. 16.9190

Answer: E

16. A manufacturer of toothpaste wishes to do a market survey on four new flavours of toothpaste to determine whether customers have a specific preference for one flavour or whether all flavours are equally well liked by customers. The four new flavours are: lemon, strawberry, peppermint and orange. 200 customers are each given a sample of all of the new flavours and are asked to state their favourite flavour. 45 customers state that they prefer the lemon flavour, 67 the strawberry flavour, 39 the peppermint flavour and 49 the orange flavour. How many customers would we expect to prefer the strawberry flavour if there was no difference in preference between the four different flavours?

a. 40

b. 50

c. 200

d. 100

e. 0

Answer: B

17. Which of the following statements regarding the Chi-square distribution is false?

a. The Chi-square goodness of fit test is always one-sided

b. The degrees of freedom for a test of association is (r-1)(c-1) in a contingency table with r rows and c columns

c. The Chi-square distribution is very skew to the left

d. The Chi-square distribution can be used to test for Normality

e. The degrees of freedom for a goodness of fit test is (k-1) where k is the number of categories used for the test

Answer: C

18. A manufacturer of toothpaste wishes to do a market survey on four new flavours of toothpaste to determine whether customers have a specific preference for one flavour or whether all flavours are equally well liked by customers. The four new flavours are: lemon, strawberry, peppermint and orange. 200 customers are each given a sample of all of the new flavours and are asked to state their favourite flavour. 45 customers state that they prefer the lemon flavour, 67 the strawberry flavour, 39 the peppermint flavour and 49 the orange flavour. What is the test statistic value for the hypothesis test in this case?

a. 8.72

b. 7.44

c. 8.08

d. 11.10

e. 9.48

Answer: A

19. A manufacturer of toothpaste wishes to do a market survey on four new flavours of toothpaste to determine whether customers have a specific preference for one flavour or whether all flavours are equally well liked by customers. The four new flavours are: lemon, strawberry, peppermint and orange. 200 customers are each given a sample of all of the new flavours and are asked to state their favourite flavour. 45 customers state that they prefer the lemon flavour, 51 the strawberry flavour, 39 the peppermint flavour and 65 the orange flavour. What is the test statistic value for the hypothesis test in this case?

a. 8.72

b. 7.44

c. 8.08

d. 11.10

e. 9.48

Answer: B

20. A manufacturer of toothpaste wishes to do a market survey on four new flavours of toothpaste to determine whether customers have a specific preference for one flavour or whether all flavours are equally well liked by customers. The four new flavours are: lemon, strawberry, peppermint and orange. 200 customers are each given a sample of all of the new flavours and are asked to state their favourite flavour. 45 customers state that they prefer the lemon flavour, 67 the strawberry flavour, 47 the peppermint flavour and 41 the orange flavour. What is the test statistic value for the hypothesis test in this case?

a. 8.72

b. 7.44

c. 8.08

d. 11.10

e. 9.48

Answer: C