the table list the distribution of educational achievement for people in the uni

Question

the table list the distribution of educational achievement for people in the united states ages 25 and older. it also list the results of a ramdom survey for two additional age groups.

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a. does the distribution for people in the united state ages 25 and older differ from the distribution for peoplein the united states age 30-34? alpha = 0.05

b. use the data for 30 to 34 year old and 65 to 69 to test whether age and educational attainment are related use alpha = 0.01

Educational attainment 25 and older 30-34 65-69 Not a high school graduate 12.40% 36 62 High school Graduate 30.40% 84 148 some college, no degree 16.70% 56 73 Associate's degree 9.60% 34 36 Bachelor's degree 19.80% 73 73 Advanced degree 11.10% 38

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Explanation / Answer

(a)

Here chi square good ness of fit test will be used.

Hypotheses are:

H0:  The distribution for people in the united state ages 25 and older do not differ from the distribution for peoplein the united states age 30-34.

Ha:The distribution for people in the united state ages 25 and older differ from the distribution for peoplein the united states age 30-34.

Following table shows the expected frequencies:

Following is the result of chi square goodness of fit test generated by excel:

The p-value is 0.5139

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

That is we cannot conclude that the distribution for people in the united state ages 25 and older differ from the distribution for peoplein the united states age 30-34.

b)

Here chi square test of independence will be used, Hypotheses are:

H0:  Age and educational attainment are independent.

Ha:  Age and educational attainment are related.

Following is the output of chi square test of independence generated by excel:

The p-value is : 0.0816

Since p-value is greater than 0.01 so we fail to reject the null hypothesis.

That is we cannot conclude that age and educational attainment are related.

Educational attainment 25 and older(p) 30-34 (O) E=p*321 Not a high school graduate 0.124 36 39.804 High school Graduate 0.304 84 97.584 some college, no degree 0.167 56 53.607 Associate's degree 0.096 34 30.816 Bachelor's degree 0.198 73 63.558 Advanced degree 0.111 38 35.631 Total 1 321 321

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