Question

7. A study of people who refused to answer survey questions provided the randomly selected sample data shown in the table below. At a = .01, test the claim the cooperation of the subject response or refusal is independent of age category.

Review for Last Test 6. A study from a university medical center examined whether the risk of hepatitis C as related to whether people had tattoos and to where they got their tattoos. Do the data indicate that the risk of hepatitis C is unrelated to tattoo status at the 5% significance level? Hepatitis C No Hepatitis C 35 Tattoo, parlor Tattoo, elsewhere None 17 12 53 22 491 7. A study of people who refused to answer survey questions provided the randomly selected sample data shown in the table below. At a = .01, test the claim the cooperation of the subject response or refusal is independent of age category. Age 60 and over 18-21 22-29 30-39 40-49 50-59 245 202 73 255 136 138 Responded 27 49 20 33 16 Refused 11 8. A child psychiatrist is studying the mental development of children. A random sample of nine children was given a standard set of questions appropriate to the age of each child. The number of irrelevant responses to the questions was recorded tor each child. 4 Age( in years) 7. 6. 10 11 12 No. of irrelevant 12 13 15 15 11 10 8 6. responses a. Does the scatterplot indicate that a linear model is probable? b. What does the coefficient of determination tell you in this problem? c. What does the slope tell you in this problem? d. Is the y-intercept helpful in this problem? Why? e. If a child is 9.5 years old, what do you predict for the number of irrelevant responses? f. Do the data indicate a strong linear relationship between age and irrelevant responses?

Answer 1

( 7 )

	Column 1	Column 2	Column 3	Column 4	Column 5	Total
Row 1	73	255	245	136	138	847
Row 2	11	20	33	16	27	107
Total	84	275	278	152	165	954

Expected Values Column 1 Column 2 Column 3 Column 5 Row 1 S44.847-74.579 27 -244.156 9713407 = 30.844 - 246.82 97807 = 31.18 Column 4 i 134.952 150x107 = 17.048 152 817 - 146.494 165.107 = 18.506 Row 2 SAX107 = 9.421 Total 275 278 165

Squared Distances Column 1 Column 2 Column 3 Column 4 Column 5 (138-146 (73–74,579) = 0.033 Row 1 (255-244.156) 244.156 0.482 (245-246.82)2 246.82 0.013 (136-134.952) 134.952 0.008 (138-146.494) 146.494 0.492 Row 2 (11-9.421) = 0.265 2 0-30.844) = 3.812 (33-31.18) = 0.106 (16-17.048) = 0.064 (27–18.506) = 3.898 13506

Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: The two variables are independent H: The two variables are dependent This corresponds to a Chi-Square test of independence. Rejection Region Based on the information provided, the significance level is a = 0.01 , the number of degrees of freedom is df = (2-1) x (5-1) = 4, so then the rejection region for this test is R = {x?: x2 > 13.277}

Test Statistics The Chi-Squared statistic is computed as follows: Bij = 0.033 +0.265 +0.482 +3.812 +0.013 +0.106 +0.008 +0.064 +0.492 +3.898 = 9.175

Decision about the null hypothesis Since it is observed that x2 = 9.175 < x2 = 13.277, it is then concluded that the null hypothesis is not rejected.

Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is  enough evidence to claim that  the cooperation of the subject response or refusal is independent of age category.  at the 0.01 significance level.