A research institute poll asked respondents if they acted to annoy a bad driver.

Question

A research institute poll asked respondents if they acted to annoy a bad driver. In the poll, n= 2455 and x=947 who said that they honked. Use a 90 % confidence level.

a) Find the best point estimate of the population proportion p.

b) Identify the value of the margin of error E.

c) Construct the confidence interval.

d) Write a statement that correctly interprets the confidence interval.

POSITIVE z Scores Standard Normal (z) Distribution: Cumulative Area from the LEFT 05 5120 5160 5199 5279 5319 5359 5478 5675 .5910 6141 6517 6879 6103 0.3 6179 6554 6915 7257 6217 6591 7019 7357 7673 7123 7454 7157 7190 7291 7422 7486 7517 7549 7910 8186 8438 8078 8106 8159 8212 8289 8315 8340 8413 8599 8810 9015 9177 9319 9441 9115 9131 9162 9192 9207 9222 9251 9418 9525 9616 9693 9452 9474 9515 9535 9625 9699 9761 9812 9854 9582 9706 9767 9817 9641 9671 9678 9713 9719 9744 9750 9788 9871 9878 2.2 9909 9913 934 9951 9911 9916 9918 9936 9941 9943 9948 9949 26 2.6 9970 9971 9973 9974 9974 9977 9978 9979 9979 9981 9989 350 and up 350 and up Standard Normal (2) Distribution: Cumulative Area from the LEFT NOTE For values of zabove 349, use09999 for the area. "Use thece commion values that nesuit from interpolation Common Cridical Values Confidence Critcal Scom 1645 09600 2575 09050 0.90 0.96 1.845 1.96 2575

Explanation / Answer

p = 947 / 2455 = 0.3857 ,n = 2455

a)
the best point estimate of the population proportion p = 0.3857

b)
z value at 90% = 1.645
ME = +/- z sqrt(p * ( 1 - p)/n)
= +/- 1.645 * sqrt ( 0.3857 * 0.6143/2455)
= +/- 0.0162

c)

CI = p + / - ME
= 0.3857 +/- 0.0162
= (0.3695 , 0.4019)
d)
we are 90% confident that the respondents honked is between 0.3695 and 0.4019

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