Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x overbar, is found to be 115, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about mu if the sample size, n, is 16. (b) Construct a 98% confidence interval about mu if the sample size, n, is 20. (c) Construct a 99% confidence interval about mu if the sample size, n, is 16. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?

Answer #1

Part a)

Confidence Interval

Lower Limit =

Lower Limit = 108.4938

Upper Limit =

Upper Limit = 121.5062

98% Confidence interval is ( 108.4938 , 121.5062 )

Part b) n = 20

Confidence Interval

Lower Limit =

Lower Limit = 109.3215

Upper Limit =

Upper Limit = 120.6785

98% Confidence interval is ( 109.3215 , 120.6785 )

Part c) n = 16

Confidence Interval

Lower Limit =

Lower Limit = 107.6332

Upper Limit =

Upper Limit = 122.3668

99% Confidence interval is ( 107.6332 , 122.3668 )

Part d)

No, because the requirement for calculating a t interval for sample size less than 30 the data should come from a population that is normally distributed.

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A simple random sample of size n is drawn from a population that
is normally distributed. The samplemean,
x overbar
,
is found to be
105
,
and the sample standarddeviation,s, is found to be
10
.
(a)Construct
an
80
%
confidence interval about
mu
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26
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(b)Construct
an
80
%
confidence interval about
mu
if the samplesize,n, is
16
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%
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is normally distributed. The sample mean, is found to be 109, and
the sample standard deviation, s, is found to be
10.
(a) Construct a 98% confidence interval about m μ if the
sample size, n, is 21.
(b) Construct a 98% confidence interval about mu μ if the
sample size, n, is 26.
(c) Construct a 99% confidence interval about mu μ if the
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is normally distributed. The sample mean, x overbar, is found to
be 110, and the sample standard deviation, s, is found to be
10.
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sample size, n, is 29.
(b) Construct an 80% confidence interval about mu if the
sample size, n, is 21.
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sample size, n,...

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is normally distributed. The sample mean, x overbar, is found to
be 109, and the sample standard deviation, s, is found to be
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sample size, n, is 18.
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