Smoking StatusFormerGiven below is the smoking status Number of Yearsby level of education for residents of Education18 years old or older living in acertain country from a randomsample of 1051 residents. Complete 13-15parts (a) and (b).CurrentNever< 1212160921831508115246213816 or more323660Click the icon to view the Chi-Square table of critical values.(a) Test whether smoking status and level of education are independent at the a = 0.05 level of significance.What are the hypotheses?O A. H,: The three smoking statuses are independent.H;: The three smoking statuses are dependent.B. Ho: Smoking status and level of education are dependent.H,: Smoking status and level of education are independent.*c. H,: Smoking status and level of education are independent.H,: Smoking status and level of education are dependent.Find the test statistic.X6 = (Round to three decimal places as needed.)%3D

In order to determine whether Smoking status and Level of education are independent or not, a chi-square test of independence needs to be conducted. In this test, there will be two types of counts, one is expected counts (denoted by E) and other is observed or actual counts (denoted by O). The test will determine whether the actual counts are significantly different from the expected count or not. If the test shows that there are evidence of significant difference in between them, then it can be concluded that the test is significant.The null hypothesis for the test can be given as, H0: Smoking status and Level of education are independent, and the alternate hypothesis for the test can be given as, Ha: Smoking status and Level of education are dependent. Hence, option (C) is correct.The observed counts for each category or cell are mentioned in the table. To calculate the expected count for all the 9 categories, use the formula, Expected counts=(Row total)·(Column total)Sample size.The table mentioned below, shows the expected count for each category after calculation. Number of years of education Current Former Never <12 160.59 95.195 179.215 12 141.393 83.815 157.792 13-15 38.763 22.978 43.259 16 or more 47.254 28.011 52.735 The value of test statistics can be calculated by using the formula, χ2=∑(Observed-Expected)2Expected. The table mentioned bellow summarizes the calculation for χ2. Calculation gives χ2≈11.385.The degrees of freedom d.f. for a test of independence can be calculated using the formula, d.f=(r-1)·(c-1). where, r is number of rows of contingency table. c is number of columns of contingency table. Calculate the required d.f. by substituting r=4 and c=3 in the above-mentioned formula for d.f. Calculation gives d.f.=6. To find the p-value, use the chi-square distribution with d.f.=6 and evaluate the proportion of data that lies beyond test statistic, χ2≈11.385. It gives p-value=0.077. The significance level is 5%, that is, α=0.05. Since p-value>α, it indicates that there is insufficient evidence against the null hypothesis. Therefore, the null hypothesis is not rejected. At α=0.05, there is insufficient evidence to conclude that Smoking status and Level of education are dependent.