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.
2. A random sample of 190 cars found that 89% had an automatic transmission. Find and
interpret the 95% confidence interval for the true proportion of cars that are automatic.
3. In a recent study of 50 American adults, it was found that they drove 16 miles to work with
a standard deviation of 2.5 miles.
a) Construct and interpret the 80% confidence interval for the average distance people
drive to work every day.
b) Does your answer change if you know the national standard deviation for miles driven
is actually 2.5? If so, find the new confidence interval, if not, explain why.
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