This is the case of finding the confidence interval for the mean when is unknown,
and this confidence interval is given by,
where,
we are given that,
and
therefore % is given by,
(a).
for a 90% confidence interval
[value generated from the t-table]
hence the required confidence interval is given by,
That is we can say with 90% confidence that the true value of the mean lies between
(b).
for a 95% confidence interval
[value generated from the t-table]
hence the required confidence interval is given by,
That is we can say with 95% confidence that the true value of the mean lies between
(c).
for a 99% confidence interval
[value generated from the t-table]
hence the required confidence interval is given by,
That is we can say with 99% confidence that the true value of the mean lies between
(d).
Now comparing the three confidence interval
a -
b -
c -
the widest interval is the 99% confidence interval that is (c) -
and the narrowest interval is the 90% confidence interval that is (a) -
Please show all work!!! 11.* A random sample of size n 64 is drawn from a...
A simple random sample of size 64 is drawn from a normal population with a known standard deviation σ. The 95% confidence interval for the population mean μ is found to be (12, 16). The approximate population standard deviation σ is:
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x̅, is found to be 107 , 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 22 .(b) Construct a 98 % confidence interval about μ if the sample size, n, is 12 .(c) Construct a 95 % confidence interval about μ if the...
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x̅, is found to be 109 , and the sample standard deviation, 5 , is found to be 12 .(a) Construct a 96 % confidence interval about μ if the sample size, n, is 23 .(b) Construct a 96 % confidence interval about μ if the sample size, n, is 16 .(c) Construct a 90 % confidence interval about μ if...
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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 115, and the sample standard deviation, s, is found to be 10 (a) Construct a 98% confidence interval about if the sample size, n, s 14 (b) Construct a 98% confidence interval about μ if the sample size, n, is 19 (c) Construct a 99% confidence interval about if the sample size, n, s 14 (d)...
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 106, and the sample standard deviation, s, is found to be 10. (a) Construct a 90% confidence interval about u if the sample size, n, is 22. (b) Construct a 90% confidence interval about u if the sample size, n, is 27. (c) Construct a 99% confidence interval about u if the sample size, n, is...
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