1. Construct a feasible test statistic. (5%)
2. How to test based on this test statistic? (5%)
A manufacturer purchases steel bars. Past experience indicates that the mean tensile
strength of all incoming shipments is 10000 psi and that the standard deviation is 400
psi. In order to make a decision about incoming shipment of steel bars, the manufacturer
set up this rule for the quality-control inspector to follow: “Take a sample of 100 steel
bars. At the 0.05 significance level if the sample mean strength significant different
from 10000 psi, reject the steel bars. Otherwise the steel bars is to be accepted.” (10%)
(一) What is the range (the minimum and maximum strength) of the sample mean
strength to be accepted?
(二) Suppose the unknown population mean of incoming steel bars is really 10120 psi.
What is the probability that the quality-control inspector will fail to reject the
shipment?
(三) Suppose the quality-control inspector takes a sample of 100 steel bars. The sample
mean strength is 9910 psi. Use the confidence interval approach to decide whether
to reject the shipment at the 0.05 significance level or not.
As part of a recent survey among dual-wage-earner couples, an industrial psychologist
found that 990 men out of the 1,500 surveyed believed the division of household duties
was fair. A sample of 1,600 women found 970 believed the division of household duties
was fair. (10%)
(一) At the 0.01 significance level, is it reasonable to conclude that the proportion of
men who believe the division of household duties is fair is larger? What is the
p-value? (State the null hypothesis, the alternate hypothesis, the critical value and
the computed test statistic)
(二) If we exchange your null hypothesis and the alternate hypothesis above, will the
conclusion be the same? Can we exchange the null hypothesis and the alternate
hypothesis?
Advertisements by a Fitness Center claim that completing its course will result in losing
weight. A random sample of eight recent participants showed the following weights
before and after completing the course. At the 0.01 significance level, can we conclude
the students lost weight? (10%)
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