Question

6. A random sample of 800 adults was asked the following question: "Do you think current laws concerning the use of cloning for medical research are too strict, too lenient, or about right?" The pollsters also classified the respondents with respect to highest education level attained: high school, 2-year college degree, 4-year college degree, or advanced degree. We wish to know if attitudes on cloning are related to education level. Strict Lenient Right 215 19 170 56 130 17 High School 84 35 82 4-Year College Advanced Degree Carry out the appropriate test. Make sure to show all steps!

PLEASE DO ALL STEPS, thank you!

Answer 1

The expected values are computed in terms of row and column totals. In fact, the formula is hi y, where Ri corresponds to the total sum of elements in row i, Ci corresponds to the total sum of elements in column j, and T is the grand total. The table below shows the calculations to obtain the table with expected values Total 469 110 257 Expected Values Row 1 Row 2 Row 3 Row 4 Total Column 1 221x46 117.783 221 11027.625 221 257 64.542 Column 2 Column 3 286 469 152.425 198.792 373110 46.625 ST 251 = 108.933 18.65 110 35.75 280-251 = 83.525 28% 44-14.3 286 880 880 880 11.05 221 373 880 Based on the observed and expected values, the squared distances can be computed according to the following formula: (E O)2/E. The table with squared distances is shown below Squared Distances Column 1 Column 2 Column 3 215-152.425)2 4 117.783 9.69 170 198.792)94.17 Row 1 17.7 25.689 19-35.75P-7848 45 35517.769 7 143 3.727 56- 46.625 (35-27.625 Row 2 1.969 S2 654.722 (20 11057.249 1.885 (130-108.933)2 Row 3 4.074 160.146 Row 4

Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: The two variables are independent Ha: 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 0.05, the number of degrees of freedom is df (4 1) x (3-1) 6, so then the rejection region for this test is R x2> 12.592 Test Statistics The Chi-Squared statistic is computed as follows: (Oi -E)2 Ei 9.69 + 1.969 + 4.722 ± 7.249 + 25.689 7.848 + 17.769 + 3.727 + 4.17 + 1.885 + 4.074 + 0.146 = 88.938 Decision about the null hypothesis Since it is observedthatx288.938>x rejected 12.592, it is then concluded that the null hypothesis is It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.05 significance level.