Question

2. The Millennial generation are less religiously active than older Amer- icans. One of the questions in the General Social Survey in 2008 was “How often does the respondent pray?" Among the 385 respondents in the survey between 18 and 30 years of age, 247 prayed at least once a week.

Please be clear in your steps and how you got the number you write down.

Answer 1

Solution: Here concept of confidence interval and plus four confidence inerval is used.

Solution - 2. (a) i- We the know that proportion p for confidence is given interval by b = 2 .S.E. (b) where at a sample proportion 2 in critical a-valve significance levd S.E.(!) is the standard error of p S.E: () = (PR IF P and Q are unknown, we use estimates of P and Qood → S.E. (b) = bg v=1-6 un who pray Sample once proportion of in a week respondents is, I þ = 247 = 0.64.16 385 to find 99% confidence ficance level x = 0.01 We have interval.

at x=0.01 Two-tailed significance Zlo.04 critical z-value level is, = 2.58 S.E. (P) = SE (B) - photo 10.6416) (1-0.6415) 385 coure = 0.0244 i 99% confidence interval is 10.6416 I (2.58 x 0.0244) ? [0.6416 + 0.0630] (0:5786, 0.7046) Large - sample 99% confidence interval for the proportion 6 of all adults between 18 and 30 years of age who pray at least once a week is (0.5786, 0.7046). If we write the interval in percentage it would be (57.864. , 70.46%).

2(6) 1 - acum To we obtain follow the plus certain four steps confidence interval which are as followrs : First we add 4 imaginary observations in total number of observations. Then we split these four observations between two successes and two failure And then calculate the sample proportion | And then we follow the usual steps to obtain confidence interval I In our given is na 385 in n and respondents who do not pray question We consider pray total observation. a shall add 4 2 of them as and 2 of them.

n = 385 +y = 389 and no. of pray respondents who = 247 +2 = 249 389 .: sample proportion (p)- 249 w = 0.6401 Critical z-value at 0.0l significance level is zool = 2.58 SE(") = bq . (0.6401) (1-0.6401) 389 0.0243 - 99% confidence interval is. þ § 260.01) SE(+) 0.6401 + (2.58 x 0.0243) 0.6401 + 0.0628 (0.5773, 0.7029) = Plus four confidence interval (0.5773, 0.7029) is If we write it would be the interval (57.73% in percentage 70.29).

If we round the 99% confidence nearest to 10th of a percent would be (57.91, 70.5.1.) interval it four to be 99% the If we round the plus confidence interval nearest of a percent it would 157.7 % , 70.3 4.) 10th