Solution:
Given,
= 31.22
= 19
n = 62
Note that, Population standard deviation() is known..So we use z distribution.
Our aim is to construct 95% confidence interval.
c = 0.95
= 1- c = 1- 0.95 = 0.05
/2 = 0.05 2 = 0.025 and 1- /2 = 0.975
Search the probability 0.975 in the Z table and see corresponding z value
= 1.96
a)
The margin of error is given by
E = /2 * ( / n )
= 1.96 * ( 19 / 62 )
= 4.73
Answer : Margin of error (E) = 4.73
b)
Now , confidence interval for mean() is given by:
( - E ) < < ( + E)
( 31.22 - 4.73 ) < < ( 31.22 + 4.73)
26.49 < < 35.95
Answer : $ 26.49 to $ 35.95
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