Question

A simple random sample of size n is drawn from a population that 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 sample size, n, is 21.

(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 = 103.4835

Upper Limit =

Upper Limit = 114.5165

98% Confidence interval is ( 103.4835 , 114.5165 )

Part b)

Confidence Interval

Lower Limit =

Lower Limit = 104.1263

Upper Limit =

Upper Limit = 113.8737

98% Confidence interval is ( 104.1263 , 113.8737 )

Part c)

Confidence Interval

Lower Limit =

Lower Limit = 102.791

Upper Limit =

Upper Limit = 115.209

99% Confidence interval is ( 102.791 , 115.209 )

Part D)

No, it is not possible to draw confidence interval if the population is not normal.

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A simple random sample of size n is drawn from a population that
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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
if the samplesize,n, is
26
.
(b)Construct
an
80
%
confidence interval about
mu
if the samplesize,n, is
16
.
(c)Construct
a
70
%
confidence interval about
mu
if the samplesize,n, is
26
.
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is normally distributed. The sample mean, x overbar, is found to
be 105, 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 26. (b) Construct a 95% confidence interval about mu
if the sample size, n, is 20. (c) Construct an 80% confidence
interval about mu if the sample size, n,...

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be 111, and the sample standard deviation, s, is found to be 10.
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size, n, is 23. (b) Construct a 96% confidence interval about mu
if the sample size, n, is 27. (c) Construct a 98% confidence
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is normally distributed. The sample mean, x overbar, is found to
be 107, and the sample standard deviation, s, is found to be 10.
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size, n, is 18.
(b) Construct a 96% confidence interval about mu if the sample
size, n, is 22.
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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
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