The Confidence interval is (0.85,1.05) which contain the sample proportion for 95%of samples size.
Confidence interval is an interval with a confidence level. Confidence interval is always constructed on basis of sample , p = sample statistic - margin of error to sample statistic + margin of error
Confidence interval for a proportion are calculated using the following formula:
p= ( p' - Z√p'(1-q')/n , p'+ Z √p'(1-p')/n ) ---(1)
where, p' ---> sample proportion for sucess
1-p' -----> sample proportion for failure
Z --> Z-value (statistic value)
n---> sample size
we have given that,
sample size ( n)=850 , sample proportion (p') = 0.95 and population proportion= 0.75
a) mean of sample of proportion is same as poplution proportion i.e 0.75 ..
1 -p' = q' = 0.05
Using the formula for margin of error ,
M .E = Z √ p'q'/n ---(2)
as the Z-value for given proportion is 13.46
putting all values in equation( 2) we get,
M.E = 13.45 √0.95×0.05/850 = 0.1005
Now, we shall calculate the confidence interval for given data
confidence interval (p)
= ( 0.95 - 0.100 , 0.95 + 0.100)
p= ( 0.85 , 1.05)
Hence,confidence interval(CI) is (0.85, 1.05).
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Complete Question:
75% of all credit card users carry a balance from month to month. a. If you randomly select 850 credit card users and will compute the sample proportion that carry a balance from month to month, what is the mean of the sample proportion? b. If you randomly select 850 credit card users, what interval will contain the sample proportion for 95% of samples of that size?