Question

If the 18-34 and 60+ age groups consisted of 340 and 150 individuals, respectively, find a 98% confidence interval for 6, the difference in proportions of those in these age groups who agreed that patriotic described them very well. b. Why can you use the method that you used in part (a)? Explain. c. If θ is the target parameter that you estimated in part (a), can you claim that θ is in the 98% d. If 0 is the target parameter that you estimated in part (a), is it true that the probability is e. Interpret the confidence interval that you obtained in part (a). f If θ is the target parameter that you estimated in part (a), how many individuals need to be confidence interval that you obtained in part (a)? approximately 0.98 that is in the 98% conference interval that you obtained in part (a)? Explain. sampled from each age group in order to have a 95% confidence interval for guesses for ps. Check to make sure that the sample sizes that you calculated in part (f) will work. to have a width of 0.2, equal sample sizes for both samples? Use the sample proportions given in the problem as g. 8.64 Ina CNNIUSA Today/Gallup Poll, 1000 Americans were asked how well the term patriotic de- scribed themselves.10 Some results from the poll are contained in the following summary table. Age Group All 18-34 60+ Very well Somewhat well 31 41 .17 Not Very wel .10 .16 .04 Not well at al 06 08 .02 53 35 .77

Answer 1

0 Answes hiven that a) The 98% confidence intesvak fos the difference in the Psopostions of she age groups 13-34 and 6o t who agseed that patsiotic descibed then vey wd is given by Hehe ni-3140 ng = 150 t.35 By substitaling thesc values and tinding the value of za/a ubing Excelwe get

(o, 35-o-73) ±2.3&6-0:35*045 0, 77 150 Hence the tontidence mtesval is -0.530018-0.31988) b) Because sample sizes ane laage binomal app yo kimation by nosmaL distsi bution co e čan nok člaim that rs in this (onsidence intenval we ane 95% confidence tha is in th's confidence, intesval d) Tyue. e) we are 95% confident that tyderofortion ties onfidene intey val