Question

Question number 2 A study sampled 350 upperclassmen (Group 1) and 250 underclassmen (Group 2) at high schools around the city of Portland. The study was performed at the end of the school year and asked each if they had used steroids at any point in the last school year. Of the upperclassmen, 23 claimed to have used steroids in the last school year, and of the underclassmen, 21 claimed to have used steroids. Run a 95% confidence interval to test for a significant difference in the proportions of students who used steroids. Enter the confidence interval - round to 3 decimal places. <pı-p:<| Can it be concluded that there is a difference in the proportions?

Answer 1

Let x, be the number of upperclassmen who claim to have used steroids in the last school year and let n be the sample size of upperclassmen. The proportion of the upperclassmen who claim to have used steroids in the last school year is given as follows: -23 350 = 0.0657 Let x, be the number of underclassmen who claim to have used steroids in the last school year and let n, be the sample size of underclassmen. The proportion of the underclassmen who claim to have used steroids in the last school year is given as follows: - 21 * 250 = 0.084 The critical value of the Z- distribution at a=0.05 level of significance is 1.96 (from the standard normal table). Thus, the 95% confidence interval is given as follows: .-9.)+2. . (1- Ôu)Þ2 (1– ô2) CI.=(.-P2)=Lapvn = (0.0657-0.084)+1.96, 0.0657(1-0.0657) 0.084(1-0.084) 350 250 =-0.0183+0.0431 =(-0.0614,0.0248) Therefore, the 95% confidence interval is -0.06

The hypotheses for testing the proportions are given as follows: H.P.-P2=0 H: P.-P280 Since the hypothesized value of the proportions lies in the confidence interval, therefore, it cannot be concluded that there is a difference in the proportions.