Question
In: Statistics and Probability
A random sample of ?n measurements was selected from a population with standard deviation ?=11.7 and...
A random sample of ?n measurements was selected from a population with standard deviation ?=11.7 and unknown mean ?. Calculate a 95% confidence interval for ? for each of the following situations:
(a) ?=60, ?=85
≤?≤
(b) ?=75, ?=85
≤?≤
(c) ?=100, ?=85
≤?≤
Solutions
Expert Solution
Solution :
Given that,
(a)
Sample size = n = 60
Z
/2
= 1.96
Margin of error = E = Z/2*
(
/
= 1.96 * (11.7 /
Margin of error = E = 3.0
At 95% confidence interval estimate of the population mean is,
- E 
+ E
85 - 3.0
85 + 3.0
82
88
(b)
Sample size = n = 75
Z/2
= 1.96
Margin of error = E = Z/2*
(
/
= 1.96 * (11.7 /
Margin of error = E = 2.6
At 95% confidence interval estimate of the population mean is,
- E
+ E
85 - 2.6
85 + 2.6
82.4
87.6
(c)
Sample size = n = 100
Z/2
= 1.96
Margin of error = E = Z/2*
(
/
= 1.96 * (11.7 /
Margin of error = E = 2.3
At 95% confidence interval estimate of the population mean is,
- E
+ E
85 - 2.3
85 + 2.3
82.7
87.3
orchestra answered 1 year agoRelated Solutions
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