please answer it by A) B) etc and do it by the right decimal places Construct a
ID: 3179023 • Letter: P
Question
please answer it by A) B) etc and do it by the right decimal places
Construct a 99% confidence interval to estimate the population mean with x = 104 and sigma = 32 for the following sample sizes. a) n = 36 b) n = 41 c) n = 67 a) With 99% confidence, when n = 36, the population mean is between the lower limit of ___ and the upper limit of ____. (Round to two decimal places as needed.) b) With 99% confidence, when n = 41, the population mean is between the lower limit of ____ and the upper limit of _____. (Round to two decimal places as needed.) c) With 99% confidence, when n = 67, the population mean is between the lower limit of ____ and the upper limit of _____. (Round to two decimal places as needed.)Explanation / Answer
a.
Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=104
Standard deviation( sd )=32
Sample Size(n)=36
Confidence Interval = [ 104 ± Z a/2 ( 32/ Sqrt ( 36) ) ]
= [ 104 - 2.58 * (5.33) , 104 + 2.58 * (5.33) ]
= [ 90.24,117.76 ]
b.
Mean(x)=104
Standard deviation( sd )=32
Sample Size(n)=41
Confidence Interval = [ 104 ± Z a/2 ( 32/ Sqrt ( 41) ) ]
= [ 104 - 2.58 * (5) , 104 + 2.58 * (5) ]
= [ 91.11,116.89 ]
c.
Sample Size(n)=67
Confidence Interval = [ 104 ± Z a/2 ( 32/ Sqrt ( 67) ) ]
= [ 104 - 2.58 * (3.91) , 104 + 2.58 * (3.91) ]
= [ 93.91,114.09 ]
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