STAT 307
Homework #6
Spring 2008
URI
Note:
Due Monday 4/7/08
- All questions should be handed in.
- Selected QUESTIONS will be graded.
1) In the following exercises concerning a one-sample z-test for a population mean the
value for the test statistic is obtained by the formula
The type of test: two-tailed, left-tailed or right-tailed is given. Determine the pvalue in each case.
a. Right-tailed test:
i. Z=2.03
ii. Z=-0.31
b. Left-tailed test:
i. Z=-1.84
ii. Z=1.25
c. Two-tailed test:
i. Z=3.08
ii. Z=-2.42
2) The mean annual consumption of beer per person in the U.S. is 22.0 gallons. A
random sample of 300 Washington D.C. residents yielded a mean annual beer
consumption of 27.8 gallons. At the 10% significance level, do the data provide
sufficient evidence to conclude that the mean annual consumption of beer per
person for the nation’s capital differs from the national mean? Use the p-value
approach to hypothesis testing. Assume that the standard deviation of annual beer
consumption for Washington D.C. residents is 55 gallons.
3) The mean daily cost of community hospitals per patient in U.S. hospitals was
$1,033 in 1997. In that same year, a random sample of 30 daily costs in Ohio
hospitals had a mean of $1,123. Assuming a population standard deviation of $350
for Ohio hospitals, do the data provide sufficient evidence to conclude that, in 1997,
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the mean daily cost in Ohio hospitals exceeded the national mean of $1,033. Perform
the required hypothesis test at the 5% significance level. Use the p-value approach to
hypothesis testing.
4) For a t-curve with df=17, use the t-table to find each t-value
a. t0.05
b. t0.025
c. t0.01
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5) Because many industrial wastes contain nutrients than enhance crop growth, efforts
are being made for environmental purposes to use such wastes on agricultural soils.
Two researchers reported their findings on experiments with brewery wastes used
for agricultural purposes in an article published in Environmental Polution (Series A),
33, pp.341-351. The researchers studied the physico-chemical properties of effluent
from Mohan Meakin Breweries Ltd (MMBL) in India. They assessed the impact of
using different concentrations of the effluent: 25%, 50%, 75% and 100%. The
following data provide the percentages of limestone in the soil obtained by using
100% effluent:
2.41 2.31 2.54 2.28 2.72
2.60 2.51 2.51 2.42 2.70
Assume the population you are sampling from is fairly normal.
a. Find a 99% confidence interval for the mean available limestone in soil
treated with 100% MMBL effluent and interpret the interval.
b. Using the confidence interval found above, does it appear that the mean
available limestone in soil treated with 100% MMBL effluent exceeds 2.30%,
the percentage ordinarily found? Explain.
6) Using the data in this question (5), do the data provide sufficient evidence to
conclude, at the 1% significance level, that the mean available limestone in soil
treated with 100% MMBL effluent exceeds 2.30%, the percentage ordinarily found?
That is, answer part (b) in this question but using a hypothesis testing approach.
7) Using the data in question (5) use Excel to find the 90% confidence interval for the
mean available limestone in soil treated with 100% MMBL effluent. Hand in the Excel
printout and write the upper and lower limits for the interval in the same printout. Show
how the limits are obtained and interpret the interval.