SOLUTION: In a survey of 225 randomly selected gun owners, it was found that 69 of them said they owned a gun primarily for protection.
Find the margin of error and 95% confidence interva
Algebra.Com
Question 1199178: In a survey of 225 randomly selected gun owners, it was found that 69 of them said they owned a gun primarily for protection.
Find the margin of error and 95% confidence interval for the percentage of all gun owners who would say that they own a gun primarily for protection. Report answers to at least 2 decimal places.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sample size = 225
p = 69/225
q = (1 - 69) / 225 = 225/225 - 69/225 = (225 - 69) / 225 = 156/225
mean = 69/225
standard error = sqrt(p*q/n) = sqrt((69/225*156/225)/225) = .0307406515.
z = (x-m)/s
z is the z-score
(x-m) is the margin of error.
s is the standard error.
your confidence interval is 95%.
at 95% confidence interval, the critical z-score is plus or minus 1.96
to find the margin of error, you only need to use the hi side z-score because the confidence interval is symmetric about the mean and the margin of error above the mean is the same as the margin of error below the mean.
formula becomes 1.96 = (x-m) / standard error which becomes 1.96 = (x-m) / .0307406515.
solve for (x-m) to get (x-m) = 1.96 * .0307406515 = .0602516769.
that should be the margin of error on either side of the mean at 95% confidence interval.
the mean is equal to 69/225
that minus the margin of error yields a low side value of .2464149897.
that plus the margin of error yields a high side value of .3669183436.
this is tested using the calculator at https://davidmlane.com/hyperstat/z_table.html
below are the results.
your solution is shown below:
the margin of error is .0602516769 at 95% confidence interval.
the 95% confidence interval is from .2464149897 to .3669183436.
let me know if you have any questions.
theo
RELATED QUESTIONS
In a survey of 300 randomly selected gun owners, it was found that 75 of them said they... (answered by Boreal)
In a survey of 94 pet owners, 57 said they own a dog, and 11 said they own a cat. 7 said... (answered by josmiceli)
In a survey of 68 pet owners, 20 said they own a dog, and 21 said they own a cat. 18 said (answered by addingup,ikleyn)
In a survey of 68 pet owners, 20 said they own a dog, and 21 said they own a cat. 18 said (answered by jorel555)
A special-interest group has conducted a survey concerning a ban on hand guns. Note: A... (answered by ewatrrr)
A survey found that 30% of pet owners had their pets bathed professionally rather than... (answered by stanbon)
69% of all Americans are home owners. If 37 Americans are randomly selected, find the... (answered by CPhill,ikleyn)
1. In a survey, 40 randomly picked people were asked if they rented or owned their own... (answered by ewatrrr)
In a survey of college graduates, 21% said they found employment in a closely related... (answered by Boreal)