Question

# A simple random sample of size n is drawn from a population that is normally distributed....

A simple random sample of size n is drawn from a population that is normally distributed. The sample? mean, is found to be 112?, and the sample standard? deviation, s, is found to be 10.

?(a) Construct a 95?% confidence interval about mu? if the sample? size, n, is 18.

?(b) Construct a 95?% confidence interval about mu? if the sample? size, n, is 11.

?(c) Construct a 70?% confidence interval about mu? if the sample? size, n, is 18.

?(d) Could we have computed the confidence intervals in parts? (a)-(c) if the population had not been normally? distributed?

Solution: = 112 = 10

( a )

n = 18

z = 1.96

95% confidence interval =  z ( / )

= 112 1.96 ( 10/ )

= 112 4.6197

= ( 107.3803 , 116.6197 )

( b )

n = 11

z = 1.96

95% confidence interval =  z ( / )

= 112 1.96 ( 11 / )

= 112 5.0817

= ( 106.9183 , 117.0817 )

( c )

n = 18

z = 1.04

95% confidence interval =  z ( / )

= 112 1.04 ( 10/ )

= 112 2.4513

= ( 109.5487 , 114.4513 )

( d )

No, the confidence interval computed in parts (a)-(c), if the popolation had not been normally distributed

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