1. The probability, ?, of a Type I error in a hypothesis test is: a) P(reject H0|H0 true)
b) P(reject HA|H0 true) c) P(do not reject H0|H0 true) d) P(do not reject H0|H0 false)
2. A factory manger thinks that on average 80 machines are assembled daily. A random sample of 12
days taken in a month gave the following results for daily assembly numbers.
77 78 78 79 80 82 85 87 90 91 92 94
a) Use the Sign test to determine whether there is sufficient evidence to conclude that the mean
number of machines assembled daily differs from 80. Use ? = .05.
b) Use the WSRT to carry out the same test.
c) Which is the better test to use in this situation? Explain.
3. Show that Y and S2
are unbiased and consistent estimators of the population mean and
population variance respectively.
4. Show that Y is an efficient estimator of the parameter ? = ? for the Poisson distribution.
5. A random sample of 144 yielded a mean of 96 and a variance of 169.
a) Test the hypothesis that the true population mean is 100 against the alternative that it is not at
the 0.01 level of significance. Use the p-value of the test to do so.
b) What is the power of the test if the true population mean is 102?
6. A shoe company has factories in Bedford, Quebec, and Prince George, British Columbia. The
company recently undertook a comparison of worker productivity for the two plants. 11 workers
were randomly selected from each plant and the number of pieces each worked on during a production
was recorded with the following results:
Plant 1 (Bedford): 24 27 23 21 24 22 26 28 27 21 29
Plant 2 (P. George): 21 20 19 23 25 24 22 27 20 18 30
If the population distributions are non-normal, test whether there is sufficient evidence at the 0.05
level of significance to conclude that average worker productivity is different for the 2 plants.
7. A particular type of steel beam has been designed to have a compressive strength of at least
50,000(lb/in2
). The compressive strength of a random sample of 25 beams was measured and is
given below. Assuming that compressive strengths have a symmetric but non-normal distribution,
test whether there is sufficient to conclude that the true mean compressive strength is less than the
specified value. Use ? = .01
di rank | di | di rank | di | di rank | di | di rank | di | di rank | di |
-10 1 -81 7 -129 13 -178 19 -229 25
-27 2 90 8 136 14 -183 20
36 3 -95 9 -150 15 -192 21
-55 4 -99 10 -155 16 -199 22
73 5 113 11 -159 17 -212 23
-77 6 -127 12 165 18 -217 2
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