Use this information to answer the next seven questions. To determine if there i

Question

Use this information to answer the next seven questions. To determine if there is an association between gender and reading habits, 270 adults are randomly sampled from across the United States and asked the following question: "How often do you read a book outside of work or school: regularly, sometimes, or never?" The results are summarized in this table. Reading Habits Regularly Sometimes Never Total Male 42 72 10 124 Female 65 74 7 146 Total 107 146 17 270

1. What are the appropriate hypotheses for this chi-square test?

H0: "There is no correlation between gender and reading habits" vs. Ha: "There is a correlation between gender and reading habits"

H0: "There is a correlation between gender and reading habits" vs. Ha: "There is no correlation between gender and reading habits"

H0: "There is an association between gender and reading habits" vs. Ha: "There is no association between gender and reading habits"

H0: "There is no association between gender and reading habits" vs. Ha: "There is an association between gender and reading habits"

2. What are the appropriate degrees of freedom for this test? Hint: df = (r 1)(c 1)

6

57

2

269

3. What is the expected count for males who answered "Never"?

5.72

12.04

7.81

10.00

4. Suppose the expected count for males who answered "Never" is 11.3. Refer to this table of expected counts. Regularly Sometimes Never Male 49.14074 67.051852 *** Female 57.85926 78.948148 9.192593 Is the sample size large enough to conduct a chi-square test?

No, not all expected counts are greater than 30.

No, not all expected counts are equal.

Yes, all expected counts are greater than 5.

Yes, the sample size is greater than 30.

5. Assume the conditions for the test are met. Refer to this table of chi-square components. Regularly Sometimes Never Male 1.027636 0.3651528 0.615757 Female *** 0.3101298 0.522971 What is the chi-square component for females who read regularly? Hint: calculate for the cell marked with ***.

0.881279

0.123416

4.562399

7.14074

6. Refer to this StatCrunch output. N DF Chi-Square P-Value 270 2 3.7329254 0.1547 What is the appropriate p-value? 3.7329254

0.025

0.1547

0.0002

7. Suppose the p-value is 0.11. At the = 0.05 level, what conclusion should be made? Fail to reject H0.

There is an association between gender and reading habits.

Fail to reject H0. There is insufficient evidence that there is an association between gender and reading habits.

Reject H0. There is an association between gender and reading habits.

Reject H0. There is no association between gender and reading habits.

8. In a chi-square test, the "expected" counts are the values we expect if there is an association between the variables.

True

False

9. A small chi-square test statistic supports the null hypothesis.

True

False

10. If a chi-square test is significant (i.e., there is an association between the variables), we should look at the conditional distributions as a follow-up analysis.

True

False

Explanation / Answer

1)
d)
H0: "There is no association between gender and reading habits" vs. Ha: "There is an association between gender and reading habits

2)
df = 2
3)
male and never
E = 17 * 124/270
= 7.81
4)
Yes, all expected counts are greater than 5

i have answered first 4 question by chegg policy . althought answer to rest questions can be calculated easily using table i have provided in beginning

c1 c2 c3 sum r1 42 72 10 124 r2 65 74 7 146 sum 107 146 17 270 Eij 1 2 3 expected 1 49.14074 67.05185 7.807407 2 57.85926 78.94815 9.192593 0i 42 72 10 65 74 7 Ei 49.14074 67.05185 7.807407 57.85926 78.94815 9.192592593 sum (Oi-Ei)^2/Ei 1.037636 0.365153 0.615757 0.881279 0.31013 0.522971319 3.732925 critical value 5.991465

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