Question

Smoking remains more common in much of Europe than in the United States. In the United States, there is a strong relationship between education and smoking: well-educated people are less likely to smoke. Does a similar relationship hold in France? Here is a two-way table of the level of education and smoking status (nonsmoker, former smoker, moderate smoker, heavy smoker) of a sample of 461 French men aged 20 to 60 years. The subjects are a random sample of men who visited a health center for a routine checkup. We are willing to consider them an SRS of men from their region of France. Smoking Status Education Nonsmoker Former Moderate Heavy Primary school 58 55 41 38 Secondary school 37 43 27 31 University 53 26 34 18 The null hypothesis states that there is no relationship between these variables. That is, the distribution of smoking is the same for all three levels of education. (a) Find the expected counts for each smoking status among men with a university education. This is one row of the two-way table of expected counts. Find the row total and verify that it agrees with the row total for the observed counts. Use two decimals for the expected counts and a whole number for the total. Smoking Status Education Nonsmoker Former Moderate Heavy TOTAL University Expected (b) We conjecture that men with a university education smoke less than the null hypothesis calls for. How does comparing the observed and expected counts in this row confirm this conjecture? Select all that apply The heavy-smoker count is less than expected. The nonsmoker count is lower than expected. The heavy-smoker count is more than expected. The nonsmoker count is higher than expected.

Answer 1

Total Education smoking status moderate Non-smoker Former Heavy 38 58 55 Primary school School 192 138 31 37 27 43 Secondary University 26 34 18 131 53 124 102 87 IN=461 148 Total Expected count, Eig= Tix Tj where Ti Total of ith row of ith column. Tj - Total N 461 Education smoking status former moderate Non-smoker Heavy Total University 53 26 34 18 131 Expected 131x148 1318124 461 1310102 131%87 461 461 42.06 35.24 28.98 24.72 131 b 7 The heavy- smoker count is less than expected, 17 The non-smoker count is higher than expected.