A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans...

Free

70.2K

Verified Solution

Question

Statistics

A newsgroup is interested in constructing a 90% confidenceinterval for the proportion of all Americans who are in favor of anew Green initiative. Of the 588 randomly selected Americanssurveyed, 354 were in favor of the initiative. Round answers to 4decimal places where possible.
a. With 90% confidence the proportion of all Americans who favorthe new Green initiative is between _? and ?_
b. If many groups of 588 randomly selected Americans weresurveyed, then a different confidence interval would be producedfrom each group. About _?_ percent of these confidenceintervals will contain the true population proportion of Americanswho favor the Green initiative and about _?_ percent will notcontain the true population proportion.

Answer & Explanation Solved by verified expert

3.9 Ratings (691 Votes)

sample success x =	354
sample sizeÂ Â Â Â Â Â Â Â Â n=	588
sample proportion pÌ‚ =x/n=	0.6020

std error se= âˆš(p*(1-p)/n) =	0.0202

for 90 % CI value of z=	1.645
margin of error E=z*std errorÂ Â =	0.0332
lower bound=pÌ‚ -EÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =	0.5688
Upper bound=pÌ‚ +EÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =	0.6352
from above 90% confidence interval for population proportion =(0.5688 ,0.6352)

If many groups of 588 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About 90%Â Â of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 10% will not contain the true population proportion

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member