Question

A simple random sample is drawn from a population for estimating the mean of the population. The mean from the sample is 25.6 and the sample size is 60.\

1. If the population standard deviation is known to be 10.5, construct a 95% confidence interval for the population mean.

2. If the population standard deviation is not known but the sample standard deviation is calculated to be 11.5, construct a 95% confidence interval for the population mean.

3. Do we need to make any assumption in constructing the confidence interval?

Answer #1

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....

A simple random sample size of 40 is drawn from a population.
The sample mean is found to be x overbar equals 120.1x=120.1
and the sample standard deviation is found to be
s equals 12.8s=12.8.
Construct a 99% confidence interval for the population
mean.

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 109, 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 14.
(c) Construct a 90% confidence interval about mu if the
sample size, n,...

A simple random sample of size nequals17 is drawn from a
population that is normally distributed. The sample mean is found
to be x overbar equals 61 and the sample standard deviation is
found to be sequals11. Construct a 95% confidence interval about
the population mean. The 95% confidence interval is ( nothing,
nothing). (Round to two decimal places as needed.)

A simple random sample of size n=15 is drawn from a population
that is normally distributed. The sample mean is found to be x
overbar=62 and the sample standard deviation is found to be s=19.
Construct a 95% confidence interval about the population mean.
The 95% confidence interval is (_,_).
(Round to two decimal places as needed.)

A simple random sample of size n is drawn from a population that
is known to be normally distributed. The sample variance is
determined to be 20.
a) Construct a 95% confidence interval for σ² if the sample size
is 40.
b) How does increasing the level of confidence affect the width
of the confidence interval?

A simple random sample of size n equals 40 is drawn from a
population. The sample mean is found to be x overbar equals 120.2
and the sample standard deviation is found to be s equals 13.2.
Construct a 99% confidence interval for the population mean.

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 111, and the sample standard deviation, s, is found to be 10.
(a) Construct a 96% confidence interval about mu if the sample
size, n, is 23. (b) Construct a 96% confidence interval about mu
if the sample size, n, is 27. (c) Construct a 98% confidence
interval about mu if the sample size, n,...

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 110, and the sample standard deviation, s, is found to be
10.
(a) Construct an 80% confidence interval about mu if the
sample size, n, is 29.
(b) Construct an 80% confidence interval about mu if the
sample size, n, is 21.
(c) Construct a 70% confidence interval about mu if the
sample size, n,...

A simple random sample of size n is drawn from a population that
is normally distributed. The sample mean, overbar x, is found to
be 115, and the sample standard deviation, s, is found to be 10.
(a) Construct a 98% confidence interval about μ if the sample
size, n, is 20. (b) Construct a 98% confidence interval about μ
if the sample size, n, is 25. (c) Construct a 99% confidence
interval about μ if the sample size, n,...

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