The health board of a major city wants to know if people who have different type
ID: 3052710 • Letter: T
Question
The health board of a major city wants to know if people who have different types of healthcare coverage (HMO, Medicate/Medicaid, or no insurance) go to different types of hospitals (privately funded, government-funded, or free clinic) when they are sick or injured. Using the data below, conduct a two-way chi-square to test the null hypothesis that type of insurance does not affect which hospital they choose. Hospital Type Insurance Type Private Public Free Clinic HMO 17 4 Medicare/Medicaid 24 30 No Insurance 14Explanation / Answer
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
H0: Insurance type does not affect the selection of hospital type.
Ha: Insurance type does affect the selection of hospital type.
Formulate an analysis plan. For this analysis, we assume the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.
Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.
Let DF is the degrees of freedom, r is the number of levels of gender, c is the number of levels of the voting preference, nr is the number of observations from level r of gender, nc is the number of observations from level c of voting preference, n is the number of observations in the sample, Er,c is the expected frequency count when gender is level r and voting preference is level c, and Or,c is the observed frequency count when gender is level r voting preference is level c.
DF = (r - 1) * (c - 1) = (3 - 1) * (3 - 1) = 4
Er,c = (nr * nc) / n
E1,1 = (27 * 49) / 120 = 11.025
E1,2 = (27 * 50) / 120 = 11.25
E1,3 = (27 * 21) / 120 = 4.725
E2,1 = (63 * 49) / 120 = 25.725
E2,2 = (63 * 50) / 120 = 26.25
E2,3 = (63 * 21) / 120 = 11.025
E3,1 = (30 * 49) / 120 = 12.25
E3,2 = (30 * 50) / 120 = 12.5
E3,3 = (30 * 21) / 120 = 5.25
?2 = ? [ (Or,c - Er,c)2 / Er,c ]
?2 = (17 - 11.025)2/11.025 + (6 - 11.25)2/11.25 + (4 - 4.725)2/4.725 + (24 - 25.725)2/25.725 + (30 - 26.25)2/26.25 + (9 - 11.025)2/11.025 + (8 - 12.25)2/12.25 + (14 - 12.5)2/12.5 + (8 - 5.25)2/5.25
= 9.917685
We use the Chi-Square Distribution Calculator to find P(?2 > 9.917685) = 0.0418.
Interpret results. Since the P-value (0.0418) is less than the significance level (0.05), we cannot accept the null hypothesis. Thus, we conclude that Insurance type does affect the selection of hospital type.
Private Public Free Clinic Total HMO 17 6 4 27 Medicare/Medicaid 24 30 9 63 No insurance 8 14 8 30 Total 49 50 21 120Related Questions
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