In a February 2005 poll conducted by the Gallup Organization, 302 of 1008 random

Question

In a February 2005 poll conducted by the Gallup Organization, 302 of 1008 randomly selected adults aged 18 or older stated that they believe the United States is spending too little on national defense. a. Obtain a point estimate for the proportion of adults aged 18 or older who feel the United States is spending too little on national defense. b. Verify that the requirements for constructing a confidence interval about P are satisfied. c. Construct a 98% confidence interval for the proportion of adults aged 18 or older who believe the United States is spending too little on national defense. INTERPRET THE INTERVAL.

Explanation / Answer

n = 1008

p = x/n = 302/1008 = 0.299

Requirements:

np(1-p) 10 and n 0.05N

(1008*0.299)(1-0.299) = 211.276 10

Therefore, conditions are satisfied to construct confidence interval.

98% Confidence interval :

p ± Z/2 [p(1-p)]/n

Z/2 = 1- (0.02/2) = 0.99

Find 0.99 from Z table. 0.99 lies between 0.9898 and 0.9901

Z score=2.32 and Z score= 2.33

(2.33+2.32)/2 = 2.325

0.299 ± 2.325(0.299)(1-0.299)/1008

0.299±0.0335

98% confidence interval = ( 0.3325,0.2655)

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