Question

send data to excel
less than high school high school college higher than college total
observed frequency ( f_o ) 20 25 123 12 180
expected frequency ( f_e ) 21.60 45.00 99.00 14.40
( \frac{(f_o - f_e)^2}{f_e} ) 0.119 8.889 5.818 0.400
part 2
answer the following to summarize the test of the hypothesis that the distribution of highest degrees earned by thinking channel viewers is the same as the distribution of highest degrees earned by american adults as a whole. use the 0.10 level of significance for the test.
(a) determine the type of test statistic to use.
type of test statistic: chi - square degrees of freedom: 4
(b) find the value of the test statistic. (round your answer to two or more decimal places.)
15.23
(c) find the critical value. (round your answer to two or more decimal places.)

(d) can we conclude that the distribution of highest degrees earned by thinking channel viewers is different from the distribution of highest degrees earned by american adults as a whole?
yes no

Explanation:

Step1: Recall chi - square critical value concept

For a chi - square test with $\alpha = 0.10$ and degrees of freedom $df=4$, we use the chi - square distribution table.

Step2: Look up critical value

Looking up in the chi - square distribution table for $\alpha = 0.10$ and $df = 4$, we find $\chi_{0.10,4}^2=7.779$.

Step3: Compare test statistic and critical value

The test statistic is $\chi^2 = 15.23$. Since $15.23>7.779$.

Answer:

(c) 7.78
(d) Yes