A person’s educational attainment and age group was collected by the U.S. Census

ID: 2946508 • Letter: A

Question

A person’s educational attainment and age group was collected by the U.S. Census Bureau in 1984 to see if age group and educational attainment are related. The counts in thousands are in following table ("Education by age," 2013):

Table: Educational Attainment and Age Group

Education

Age Group

Row Total

25-34

35-44

45-54

55-64

>64

Did not complete HS

5416

5030

5777

7606

13746

37575

Competed HS

16431

1855

9435

8795

7558

44074

College 1-3 years

8555

5576

3124

2524

2503

22282

College 4 or more years

9771

7596

3904

3109

2483

26863

Column Total

40173

20057

22240

22034

26290

130794

Do the data show that educational attainment and age are independent? Test at the 5% level.

(i) Which of the following statements correctly defines the null hypothesis HO?

A. level of educational attainment is not independent of age

B. level of educational attainment is independent of age

C. neither of these statements is correct for HO

Enter letter corresponding to correct answer

(ii) Which of the following statements correctly defines the alternate hypothesis HA?

A. level of educational attainment is not independent of age

B. level of educational attainment is independent of age

C. neither of these statements is correct for HO

Enter letter corresponding to correct answer

(iii) Enter the level of significance ? used for this test:

Enter in decimal form. Examples of correctly entered answers: 0.01 0.02 0.05 0.10

(iv) Are any of the expected frequency values (for which HO is true) for any cell in your table less than 5? Calculate the expected frequencies using technology, the select most correct answer:

A. yes - this will not affect results of hypothesis test

B. yes - this may invalidate results of hypothesis test

C. no - this will not affect results of hypothesis test

D. no - this may invalidate results of hypothesis test

Enter letter corresponding to correct answer. Recommend using (Chi-Square Test of Independence Applet) to create contingency table of expected and observed frequency values in order to answer this question.

(v) Using calculator, spreadsheet, or online calculator, determine test statistic:

Enter value to nearest integer.

Recommended online calculator: Chi-Square Test of Independence Applet

(vi) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest ten-thousandth. Examples of correctly entered answers:

0.0001 0.0021 0.0305 0.6004 0.8143 1.0000

Recommended online calculator: Chi-Square Test of Independence Applet

(vii) Comparing p-value and ? value, which is the correct decision to make for this hypothesis test?

A. Accept Ho

B. Accept HA

C. Reject Ho

D. Fail to reject Ho

Enter letter corresponding to correct answer.

(viii) Select the statement that most correctly interprets the result of this test:

A. The result is statistically significant at .05 level of significance. There is not enough evidence to support the claim that level of educational attainment and age are NOT independent.

B. The result is statistically significant at .05 level of significance. Sufficient evidence exists to support the claim that level of educational attainment and age are NOT independent.

C. The result is not statistically significant at .05 level of significance. Sufficient evidence exists to support the claim that level of educational attainment and age are NOT independent.

D. The result is not statistically significant at .05 level of significance. There is not enough evidence to support the claim that level of educational attainment and age are NOT independent.

Enter letter corresponding to most correct answer