Question

1. In May 2004, a Gallup Poll of adults’ attitudes toward Health Maintenance Organizations (HMOs) found that 40% of adults had little or no confidence in HMOs, 39% had some confidence, 18% had a great deal of confidence, and 3% had no opinion (USA Today, June 22, 2004). The letters L, S, G, and N will be used to denote these percentages. A recent random sample of 500 adults gave the following distribution of responses.

   L         S     G N

212 198   82 8 Total 500

Perform a Chi Square test using the .01 significance to test the hypothesis (Ho): The current distribution of adults’ attitudes toward HMOs is the same as that of 2004.

a. Find the Critical value (table Value) for Chi square

b. Calculate the Chi Square test statistic for the sample

c. Do you reject or not reject the Ho (Explain what your answer means)

Answer 1

The hypotheses are

The observed counts in a sample of 500 adults is

Level of confidence	Observed count (O)
L	212
S	198
G	82
N	8
	500

The distribution of level of confidence as per 2004 survey is

Level of confidence	2004 distribution
L	40%
S	39%
G	18%
N	3%

If we multiply these by the total number surveyed, 500 we will get the expected count

Level of confidence	2004 distribution	Expected Count (E)
L	40%	500*0.4=200
S	39%	500*0.39=195
G	18%	500*0.18=90
N	3%	500*0.03=15

That is, the observed and Expected counts are

Level of confidence	Observed count (O)	Expected Count (E)
L	212	200
S	198	195
G	82	90
N	8	15

a. Find the Critical value (table Value) for Chi square

The significance level is . The number of levels are 4. The degrees of freedom are 4-1=3

The critical value is

Using the chi-square table for df=3 and the area under the right tail=0.01, we get the critical value=11.345

ans: the Critical value (table Value) for Chi square is 11.345

b. Calculate the Chi Square test statistic for the sample

The chi-square statistic is

ans: the Chi Square test statistic for the sample is 4.744

c. Do you reject or not reject the Ho (Explain what your answer means)

We will reject the null hypothesis, if the tets statistic is greater than the critical value. Here, the test statistic is 4.744 and it is not greater than 11.354. Hence we do not reject the null hypothesis.

ans: We do not reject the Ho. The current distribution of adults’ attitudes toward HMOs is the same as that of 2004.