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# Construct confidence intervals for various significances

A polling company split a random sample in half and asked 477 respondents the question generally speaking, do you believe the death is applied fairly or unfairly in this country today? The pollesters asked the other 477 respondents the question, generally speaking do you believe the death penalty is applied unfairly or fairly in this country today? This seems like the same question but sometimes the order of the choices matter. Of those asked the first question, 52% said they thought the death penalty was fairly applied. Of those asked the second question 63% said the same thing.
If one combines the 2 groups considering the overall group to be 1 random sample of 954 respondents what is a 95% confidence interval for the proportion of the general public that thinks the death penalty is being fairly applied?
(_______,__________)

A recent study 2500 children randomly selected found 19% of them deficient in vitamin D.
A) Construct the 98% confidence interval for the true proportion of children who are deficient in vitamin D (_______,__________)

Wild life biologist inspect 135 deer taken by hunters and find 22 of them carrying ticks that test positive for Lyme disease.
A) Create a 90% confidence interval for the percentage of deer that may carry such ticks! (_______%, _______%)
B) If the scientist want to cut the margin of error in half how many deer must they inspect?

#### Solution Preview

A polling company split a random sample in half and asked 477 respondents the question generally speaking, do you believe the death is applied fairly or unfairly in this country today? The pollesters asked the other 477 respondents the question, generally speaking do you believe the death penalty is applied unfairly or fairly in this country today? This seems like the same question but sometimes the order of the choices matter. Of those asked the first question, 52% said they thought the death penalty was fairly applied. Of those asked the second question 63% said the ...

#### Solution Summary

The solution gives detailed steps on constructing confidence intervals for proportions under 90%, 95% and 98% significance level respectively.

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