Question

please show all work

Question 3 (13 points) In a survey of 1002 people, 70% said that they voted in a recent presidential election. Answer the questions to construct and interpret a 95% confidence interval for the true percentage of people who say they voted. a. (1 pt.) What parameter are you estimating? (p or u) b. (1 pt.) Give the point estimate that you will use. c. (3 pts.) Compute the margin of error. Show your work! d. (1 pt.) Construct the confidence interval. e. (2 pts.) Give an interpretation of your confidence interval that relates back to the context/story of the problem like we did in class. f. (5 pts.) Suppose you made a 99% confidence interval instead here. How would it compare to the 95% interval you made in this question? How do you know?

Answer 1

21 n = 1002 P=0.70 The Cla) 4.1 (I for Pris is Zan I PCI-p} In) istosroilo nuomo rosoroll Parameter is P P: Pop Wation proportion of they voted in a recent preapdeatical people said clean. who will dr pointestimate of pis ² h = 0.70 c) morgin of ener. Eu tin € San Paip ka= 0.95 (for 95 % (.I.) & -0.05, 20 = 0.025 Zara 10.025 = 11.96 from std parma Pol-p) table 0.7610.30 1002 0:21 TOOL n Jo.00011 10.0145o - I d) .The 1.964 0.0145 = 0.0284 0.03 Inova 95 4. c.%. for p ř I morgin of ener) 0.70 + 0.03) 0.70 -0.03,0:70 + 0.03) (0.67,0.739.00

The 95 % confidence interval for P is(0.67,0.73)

e) Interpritation:- We are 95% confident that the true proportion of the people voted in the presidential election is in the interval(0.67,0.73)

f) The 99% confidence interval will be wider than the 95% confidence interval.

Because in the 99% confidence interval our confidence level; is increases from 95 to 99%. so the as confidence level increases the confidence interval becomes more wider & result will be more accurate.