The 99% confidence interval for a population mean is (207, 227). For a sample data the
sample mean is 217 and the population standard deviation value is 46. Compute the
sample size necessary to produce the confidence interval.
140.8
a)
b)
141.8
139.8.
Cannot determine.
d)
Answers
Given : The 99% confidence interval for a population mean is (207, 227).
For a sample data the sample mean is 217 and the population standard deviation value is 46.
To find : sample size necessary to produce the confidence interval.
Solution:
The 99% confidence interval for a population mean is (207, 227).
Z score = -2.576 to 2.576
Mean = 217
SE = Standard Error
2.58 = ( 227 - 217 ) / SE
=> SE = 10/ 2.58
SE = SD of population / √n
n = Sample Size
=> 10/ 2.58 = 46/ √n
=> √n = 11.868
=> n = 140.8
Hence the sample size necessary to produce the confidence interval. is 140.8
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