Question

Education Level and Health Insurance A researcher wishes to see if the number of adults who
do not have health insurance is equally distributed among three categories (less than 12 years of education, 12 years of education, more than 12 years of education) A sample of 60 adults who do not have health insurance is selected, and the results are shown. At a _ 0.05 can it be concluded that the frequencies are not equal? Use the P-value method. If the null hypothesis is rejected, give a possible reason for this. Less than More than Category 12 years 12 years 12 years Frequency 29 20 11 a. State the hypotheses and identify the claim. b. Find the critical value. c. Compute the test value. d. Make the decision. e. Summarize the results. Please show the work. I am not understanding this.

Answer 1

a)Ho: the frequencies for each category are equal

Ha: the frequencies for each category are not equal

b) critical value is chi square with n-1=3-1=2 degrees of freedom and α=0.05, which is 5.991

c) if there were equally distributed , the probabilities for each would be 1/3,1/3,1/3
So the expected frequencies would be 20,20,20

Chi square=Σ(observed-expected)²/expected=(29-20)²/20+(20-20)²/20+(11-20)²/20=81/20+81/20=162/20=8.1

d) 8.1>5.9 so we are in the rejection region

we reject the null hypothesis

e) there is significant evidence that the frequencies for categories less than 12, equal to 12 and more than 12 are not equal