This was on whole queston about finding margin error & confidence levels in my s

Question

This was on whole queston about finding margin error & confidence levels in my statistics exam & he had 5 parts with different type of problems in each. I need help solving these !!

Thank you !!!

Part A: If n=270 and ˆpp^ (p-hat) =0.74, find the margin of error at a 99% confidence level

Give your answer to three decimals

Part B:

In a recent poll, 480 people were asked if they liked dogs, and 66% said they did. Find the margin of error of this poll, at the 95% confidence level.

Give your answer to three decimals

Part C: If n=380 and ˆpp^ (p-hat) = 0.69, construct a 90% confidence interval.

Give your answers to three decimals

? < p > ?

Part D:Out of 200 people sampled, 98 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids.

Give your answers as decimals, to three places

? < p > ?

Part E:

A political candidate has asked you to conduct a poll to determine what percentage of people support her.

If the candidate only wants a 9% margin of error at a 90% confidence level, what size of sample is needed?

Give your answer in whole people.

Explanation / Answer

Solution:-

Part A: n=270 and p^ (p-hat) =0.74, Z = 2.58

the margin of error at a 99% confidence level : Z *sqrt(p^q^/n) = 2.58 *sqrt(0.74*0.26/270) = 0.0689

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Part B : n = 480 p = 0.66 Z = 1.96

95% confidence interval for the marign of error : 1.96*sqrt(0.66*0.34/480) = 0.0424

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Part C :   n=380 , p^ (p-hat) = 0.69,Z = 1.645

90% confidence interval. : p^ +/- Z*sqrt(p^q^/n)

= 0.69 +/- 1.645*sqrt(0.69*0.31/380)

= 0.6510 , 0.7290

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Part D:   200 people sampled, 98 had kids.

p = X/n = 98 /200 = 0.49

q = 1-p = 1-0.49 = 0.51

Z = 2.58

99% confidence interval: 0.49 +/- 2.58*sqrt(0.49*0.51/200)

: 0.3988 , 0.5812

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Part E :

p=0.5 , because nothing is told.
q=1-0.5=0.5
margin of error=5%=0.09
z = 1.65 at 90% confidence.

margin of error, e= sqrt(p(1-p)/n)*z_c
or, 0.05=sqrt(0.5*0.5/n)*1.65
or, n= (0.5*0.5*1.65/0.09)^2= 21

n = 21

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