Download T-Distribution Worksheet #1-4

Name: __________________________
t-Distribution – Worksheet #1
Date: ______________
Hour: _____
Complete all work on separate paper, please!
1.
a. Find the t-value such that the area in the right tail is 0.10 with 25 degrees of freedom.
b. Find the t-value such that the area in the right tail is 0.05 with 30 degrees of freedom.
c. Find the t-value such that the area LEFT of the t-value is 0.01 with 18 degrees of
freedom.
d. Find the critical t-value that corresponds to 90% confidence. Assume 20 degrees of
freedom.
2.
A simple random sample of size n is drawn from a population that is Normally distributed.
The sample mean is found to be 108, and the sample standard deviation is found to be 10.
a. Construct a 96% confidence interval about  if the sample size is 25.
b. Construct a 96% confidence interval about  if the sample size is 10.
c. Compare your results from Parts (a) and (b). How does decreasing the sample size
affect the margin of error?
d. Construct a 90% confidence interval about  if the sample size is 25.
e. Compare your results from Parts (a) and (d). How does decreasing the level of
confidence affect the margin of error?
f. Could we have computed the confidence intervals in Parts (a), (b), and (d) if the
population had not been Normally distributed? Why or why not?
3.
A simple random sample of size n is drawn. The sample mean is found to be 18.4, and the
sample standard deviation is found to be 4.5
a. Construct a 95% confidence interval about  if the sample size is 35.
b. Construct a 95% confidence interval about  if the sample size is 50.
c. Compare your results from Parts (a) and (b). How does increasing the sample size
affect the margin of error?
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d. Construct a 99% confidence interval about  if the sample size is 35.
e. Compare your results from Parts (a) and (d). How does increasing the level of
confidence affect the margin of error?
f. If the sample size is n = 15, what condition must be satisfied to compute the confidence
interval?
4.
For a simple random sample of 40 Honda Accords (4 cylinder, 2.4 liter, 5-speed
automatic), the mean gas mileage was 23 miles per gallon with a standard deviation of 1.5
miles per gallon. Construct a 95% confidence interval for the mean gas mileage of similar
2005 Honda Accords.
5.
The following data represent the age (in weeks) at which babies first crawl based on a
survey of 12 mothers conducted by Essential Baby:
52
30
44
35
47
37
56
26
39
26
39
28
a. Find the mean of the sample.
b. Find the standard deviation of the sample.
c. Construct a 95 percent confidence interval estimate for the mean age at which a baby
first crawls. (Assume the data comes from a Normal distribution.)
6.
The following data represent the asking price of a simple random sample of homes for sale
in Lexington, Kentucky, in June, 2005:
$227,900
$239,900
$143,000
$219,900
$459,900
$159,900
$299,900
$187,500
$205,800
$264,900
$147,800
$279,900
a. Determine which number is the outlier. Be sure to confirm it!
b. Construct a 99% confidence interval with the outlier included.
c. Construct a 99% confidence interval with the outlier removed.
d. What effect does an outlier have on the confidence interval?
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