Question

Do different types of hospitals have different practices when submitting insurance claims? Suppose an insurance examiner and his team compare the results of 27126 randomly selected health insurance claims to actual patient records. Insurance claims in the study came from three types of hospitals: public, private, and university hospitals. Of the 27126 claims evaluated, 15012 were confirmed to be accurate, 4981 contained errors but did not require recoding of the healthcare services provided, and 7133 were incorrect and required recoding of services billed. Data on the status of insurance claims are shown as a 3×3 contingency table.

	Confirmed accurate	Inaccurate, no change needed	Incorrect, recoding needed	All
Public	13278	4358	6359	23995
Private	405	134	192	731
University	1329	489	582	2400
All	15012	4981	7133	27126

The examiner uses a chi‑square test of independence at a significance level of ?=0.10α=0.10 to evaluate his null and alternative hypotheses.

?0?1:There is no association between hospital type and insurance claim status.:There is an association between hospital type and insurance claim status.H0:There is no association between hospital type and insurance claim status.H1:There is an association between hospital type and insurance claim status.

The value of his chi‑square statistic ?2χ2 is 10.02552 with four degrees of freedom. Complete the analysis by computing the ?-valueP-value of the examiner’s test and then decide whether he should reject his null hypothesis.

Compute the ?-valueP-value of the examiner’s test using software or a table of chi‑square critical values. Report your results to two decimal places.

?-value=P-value=

Should the examiner reject his null hypothesis if his significance level is ?=0.10α=0.10?

Yes. Since the ?-valueP-value of the test is greater than the stated alpha level of 0.10, there is sufficient evidence to reject the null hypothesis that hospital type and insurance claim status are unassociated.

No. Since the ?-valueP-value of the test is greater than the stated alpha level of 0.10, there is insufficient evidence to reject the null hypothesis that hospital type and insurance claim status are unassociated.

Yes. Since the ?-valueP-value of the test is less than the stated alpha level of 0.10, there is sufficient evidence to reject the null hypothesis that hospital type and insurance claim status are unassociated.

No. Since the ?-valueP-value of the test is less than the stated alpha level of 0.10, there is insufficient evidence to reject the null hypothesis that hospital type and insurance claim status are unassociated.

Answer 1