Question 1
Solution:
Confidence interval for Population mean is given as below:
Confidence interval = x̄ ± Z*σ/sqrt(n)
From given data, we have
x̄ = 55051
σ = 7568
n = 25
Confidence level = 90%
Critical Z value = 1.6449
(by using z-table)
Confidence interval = x̄ ± Z*σ/sqrt(n)
Confidence interval = 55051 ± 1.6449*7568/sqrt(25)
Confidence interval = 55051 ± 2489.6504
Lower limit = 55051 - 2489.6504 = 52561.3496
Upper limit = 55051 + 2489.6504 = 57540.6504
Confidence interval = (52561.3496, 57540.6504)
Question 2
The sample size formula is given as below:
n = (Z*σ/E)^2
We are given
Population standard deviation = σ = 7568
Confidence level = 88%
Critical Z value = 1.5548
(by using z-table/excel)
Margin of error = E = 1000
The sample size is given as below:
n = (Z*σ/E)^2
n = (1.5548*7568/1000)^2
n = 138.4559
n = 139
Required sample size = 139
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