Question

The Pew Internet and American Life Project reported on the widespread use of the Internet to search for information regarding experimental treatments or medicines. From telephone interviews of 1061 adult Internet users, it was found that 195 had searched for information on experimental treatments or medicines in the past year. • We are 96% confident that the true proportion of adult Internet users who had searched for information on experimental treatments or medicines in the past year is between % and %. (After converting to percentages, round the limits of your interval to two decimal places.) . If the study were repeated with a sample of 1198 adult Internet users, what would happen to the margin of error for the interval? the margin of error would not be affected glec the margin of error would increase the margin of error would decrease • Based on the interval calculated, could one conclude less than 20% of adult Internet users have searched for information on experimental treatments or medicines in the past year? Explain. No because both limits of the interval are below 20%. Yes because the lower limit of the interval is less than 20%. Yes because both limits of the interval are below 20%. No because the upper limit of the interval is greater than 20% while the lower limit is less than 20%.

Answer 1

Given that, x 195,n 1061 195 0.1 838 p = 1061 Level of significance,a- 1-confidence level 1 0.96 =0.04 Critical values: By using the standard normal table of Z, the critical value for two tailed test(tz004/2 is+2.054 96% Confidence interval for the proportion is: P(1- ) 96%CI pt a/ n 0.1838(1-0.1838) =0.1838 t1.96 x 1061 = (0.1594,0.2082) (15.94%, 20.82%) Hence, the 96% confidence interval for proportion is 15.94% and 20.82% As increasing the sample size 1061 to 1198, the margin of error decreases to 0.0244 to 0.0219 The margin of error would decrease Yes, because the lower limit of interval is less than 20%