A factory owner randomly selected 20 bolts made by the machines in his shop. These machines are meant to have a normal distribution with mean 8mm and standard deviation .05 mm. He recorded his data in the table below. 8.01 8.03 7.96 7.99 7.95 8.02 8.03 8.02 8.04 8.01 7.99 7.97 7.98 7.96 8.01 7.98 7.92 7.97 8.05 8.01 a) Verify that all conditions are met to construct a sampling distribution of sample means using ? = 20. Describe the sampling distribution. b) Using ? = 0.1, perform a hypothesis test to determine whether this machine is malfunctioning. Be sure to include all relevant values (hypotheses, critical values, test statistics, etc) c) Interpret the results of your hypothesis test.
A factory owner randomly selected 20 bolts made by the machines in his shop. These
machines are meant to have a
.05 mm. He recorded his data in the table below.
8.01 8.03 7.96 7.99 7.95
8.02 8.03 8.02 8.04 8.01
7.99 7.97 7.98 7.96 8.01
7.98 7.92 7.97 8.05 8.01
a) Verify that all conditions are met to construct a sampling distribution of sample means
using ? = 20. Describe the sampling distribution.
b) Using ? = 0.1, perform a hypothesis test to determine whether this machine is
malfunctioning. Be sure to include all relevant values (hypotheses, critical values, test
statistics, etc)
c) Interpret the results of your hypothesis test.
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