Question

1. A sample size of n = 70 is drawn from a population with proportion p = 0.32. Let p̂ be the sample proportion.

- Find p̂m and p̂s . Round the standard deviation to four decimal places.
- Find )28.0p̂P ( > .
- Find )40.0p̂P ( <

2. On a certain television channel, 20% of the commercials are local advertisers. A sample of 150 commercials is selected. Would it be unusual for more than 26% of the commercials to be local advertisers? Be sure to support your answer.

3. In a sample of 78 young adults, the average time per day spent sleeping was 7.09 hours. Assume the population standard deviation is 1.15 hours.

- Construct a 90% confidence interval for the mean time spent sleeping. Round your result to three decimal digits.
- Some health experts recommend that people get 8 hours or more of sleep per night. Based on your confidence interval, is it reasonable to believe that the mean number of hours of sleep for young people is 8 or more hours?
- How large would the sample have to be so that a 95% confidence interval would have a margin of error of 0.2?

4. According to a national report, a sample of 95 men aged 20-29 years had a mean waist size of 36.7 inches with a standard deviation of 8.9 inches.

- Construct a 98% confidence interval for the mean waist size. Round your results to two decimal digits.
- The results of a different study suggested the mean waist size is 38.7 inches. Based on your confidence interval, is it reasonable to believe that the mean waist size may be 38.7 inches?

5. If we increase the confidence level and keep the sample size the same, we (circlene) increase / decrease the margin of error.

Answer #1

A simple random sample of size n = 14 is drawn from a population
that is normally distributed. The sample mean is found to be x = 56
and the sample standard deviation is found to be s = 11. Construct
a 90% confidence interval about the population mean. The 90%
confidence interval is

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 equals n=40 is drawn from a
population. The sample mean is found to be x=120.4 and the sample
standard deviation is found to be s equals s=12.5. Construct a 99%
confidence interval for the population mean.
a) The lower bound is __
b) The upper bound is ___
(Round to two decimal places as needed.)

A simple random sample of size n equals 40 is drawn from a
population. The sample mean is found to be x overbar equals 121.4
and the sample standard deviation is found to be s equals 12.4.
Construct a 99% confidence interval for the population mean.
The lower bound is ?. (Round to two decimal places as
needed.)
The upper bound is ?. (Round to two decimal places as
needed.)

A simple random sample of size n is drawn from a population that
is normally distributed. The sample mean, x overbarx, is found to
be 112, and the sample standard deviation, s, is found to be 10.
(a) Construct aa 98% confidence interval about muμ if the
sample size, n, is 26.
(b) Construct aa 98% confidence interval about muμ if the
sample size, n, is 12.
(c) Construct aa 90% confidence interval about muμ if the
sample...

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 105, and the sample standard deviation, s, is found to be 10.
(a) Construct a 90% confidence interval about mu if the sample
size, n, is 24. (b) Construct a 90% confidence interval about mu
if the sample size, n, is 20. (c) Construct an 80% confidence
interval about mu if the sample size, n,...

The
Research Center interviewed a random sample of 1,546 adult
Anericans to determine the average time they spent sleeping per
night. The sample mean was found to be 7.2 hours of sleep, with a
sample standard deviation of 1.4 hours. Construct a 95% confidence
interval for the true mean. Interpret for confidence interval in
words.

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 sample of size n=100 is drawn from a normal population whose
standard deviation is o=9.4. The sample mean is x=42.53.
Part 1 of 2
(a) Construct a 80% confidence interval for u. Round the answer to
at least two decimal places.
An 80% confidence interval for the mean is __<u<__.
Part 2 of 2
(b) If the population were not approximately normal, would the
confidence interval constructed in part (a) be valid Explain.
The confidence interval constructed in...

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,...

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