You want to determine whether the reasons given by workers for continuing their education is related to job type. In the study, you randomly collect the data shown in the contingency table. At alpha = 0.05, can you conclude that the reason and type of worker are dependent? Reasons
Type of worker Professional Personal Both
Technical 37 48 40
Other 45 25 36
Complete parts (a) through (d).
(a) Identify the claim and state the null and alternative hypotheses H_0: Reasons are the type of worker. H_a: Reasons are the type of worker. The is the claim.
(b) Determine the degrees of freedom, find the critical value, and identify the rejection region. What are the degrees of freedom? Find the critical value
Choose the correct rejection region below.
A. chi^2 lessthanorequalto chi_0^2
B. chi^2 greaterthanorequalto chi_0^2
C. chi^2 > chi_0^2
D. chi^2 < chi_0^2
(c) Calculate the test statistic. If convenient, use technology. Chi^2 = (Round to three decimal places as needed.)
(d) Decide to reject or fail to reject the null hypothesis. Can you conclude that the reason and type of worker are dependent? Choose the correct conclusion below.
A. Reject the null hypothesis. There is not enough evidence to conclude that reasons are dependent on the type of worker. B. Fail to reject the null hypothesis. There is enough evidence to conclude that reasons are dependent on the type of worker.