Quiz: Chi-Square (X2)

1. The correct formula to compute a chi-square statistic is
a. equation
b. equation
c. equation

The table below shows the results for 60 rolls of a die. The sample will be used to test if the die is fair. Use this table for questions 2 through 8.

equation

2. The null hypothesis would state that the population proportion for each result is
a. 1/60
b. 1/6
c. 10
3. The expected count for each result is
a. 1/6
b. 10
c. 60
4. When the chi-square test statistic is computed, the term from the result that the die result is “1” is
a. 0.2
b. 0.4
c. 4.0
5. The chi-square test statistic is
a. 0
b. 3.0
c. 3.4
6. The degree of freedom is
a. 5
b. 6
c. 59
7. The p-value is
a. between 0.05 and 0.10
b. between 0.15 and 0.20
c. greater than 0.25
8. The best conclusion is
a. there is no significant evidence that the die is unfair.
b. there is significant evidence that the die is unfair.
c. there is proof that the die is fair.

A soft drink company has a promotion with a message printed on the cap of each bottle. The company claims that 5% of caps will win a video game, 45% will win a free bottle, and 50% say “sorry, please play again.” A random sample of 200 bottles had 8 bottles win the video game, 84 win a free bottle, and 108 did not win. A test will be conducted to test the company's claim. Use this data for questions 9 through 13.

9. A The null hypothesis would state that the proportions are
a. 0.04, 0.42, 0.54
b. 0.05, 0.45, 0.50
c. 0.33, 0.33, 0.33
10. The expected values are
a. 8, 84, 108
b. 10, 90, 100
c. 66.67, 66.67, 66.67
11. When the chi-square test statistic is computed, the term from the result “win a free bottle” is
a. –0.067
b. 0.40
c. 36.0
12. The chi-square test statistic is
a. 0.34
b. 1.00
c. 1.44
13. The p-value is
a. between 0.05 and 0.10
b. between 0.15 and 0.20
c. greater than 0.25

The table below shows the gender and selected drink of 100 persons randomly sampled to chose between two coffee drinks, A and B. A test of independence is done. Use this data for questions 14 through 21.

equation

14. A correct null hypothesis is
a. gender and drink choice are associated.
b. gender and drink choice are dependent.
c. gender and drink choice are independent.
15. The expected count for Women and Drink B is
a. 25
b. 30
c. 33
16. When the chi-square test statistic is computed, the term from the result “Men and Drink A” is
a. 0
b. 1.25
c. 2.722
17. The chi-square test statistic is
a. 8.25
b. 9.17
c. 14.00
18. The degree of freedom is
a. 1
b. 3
c. 99
19. The p-value is
a. between 0.0025 and 0.005.
b. between 0.005 and 0.01.
c. between 0.01 and 0.05.
20. The conclusion is
a. fail to reject the null hypothesis.
b. reject the null hypothesis.
c. accept the null hypothesis.
21. The tests results
a. are evidence that gender and drink choice are independent.
b. are evidence that gender and drink choice are not independent.
c. do not have any strong evidence.

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