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Additional Final Review (Ch.8-1O)<br />
When constructing a confidence interval or conducting a hypothesis test, first determine<br />
which distribution (normal or t) should be used based on the information that yOu’re<br />
given.<br />
1. What are the similarities and differences of a normal distribution and a t distribution?<br />
Under what circumstances should you use each?<br />
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A simple random sample is taken in order to obtain a 95% confidence interval for the<br />
population mean Assuming that the distribution takes on the normal shape, if the<br />
sample size is n = 9, the sample mean is 1 = 22, and the standard deviation of the<br />
sample is s = 6.3, what is the 95% confidence interval?<br />
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3. Consider a researcher wishing to estimate the proportion of X-ray machines that<br />
malfunction and produce excess radiation. A random sample of 40 machines is taken<br />
and 12 of the machines malfunction. Construct the 95% confidence interval.<br />
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iron club at a speed of 90 miles per hour. He had a golf equipment lab test a low<br />
significance level to determine whether the ball meets the golfer’s requirements.<br />
concerned.<br />
The sample resulted in a sample mean of 163.2 yards with a sample standard<br />
compression ball by having a robot swing his club 8 times at the required speed.<br />
5. An insurance company is reviewing its current policyr4ates, When originally setting<br />
4. A golfer wishes to find a ball that will travel more than 160 yards when hit with his 7-<br />
the rates they believed that the average claim amount was $1,800. They are concerned<br />
of money. They randomly select 40 claims, and calculated a sample mean of $1,950<br />
that the true mean is actually higher than this, because they could potentially lose a lot<br />
with a standard deviation of $500. Test to see if the insurance company should be<br />
deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05
6. Trying to encourage people to stop driving to campus, the university claims that on<br />
average it takes people 30 minutes to find a parking space on campus. I don’t think it<br />
takes so long to find a spot. In fact I have a sample of the last five times I drove to<br />
campus, and I calculated the mean time to be 20 minutes. Assuming that the time<br />
it takes to find a parking spot is normal, and that the standard deviation of the sample<br />
is 6 minutes, perform a hypothesis test at the .05 significance level to see if my claim<br />
is correct.<br />
7. Suppose that you interview 1000 exiting voters about who they voted for governor.<br />
Of the 1000 voters, 550 reported that they voted for the democratic candidate. Is<br />
there sufficient evidence to suggest that the democratic candidate will win the<br />
election at the .01 level?
0.01. Assume that a = 4.8 minutes.<br />
of 50 calls originating in the town was 8.6 minutes. Does the data provide sufficient<br />
of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of<br />
evidence to conclude that the mean call duration, , is different from the 1990 mean<br />
was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis<br />
‘ 9. A sample of 10 sales receipts from a grocery store has a mean of $137 and a standard<br />
grocery store are different from $150. Test at the .05 significance level.<br />
deviation of $30. Use these values to test whether or not the mean in sales at the<br />
test to determine whether the average duration of long-distance phone calls has<br />
changed from the 1990 mean of 9.4 minutes. The mean duration for a random sample<br />
8. In 1990, the average duration of long-distance telephone calls originating in one town
10. In a quality control situation, the mean weight of objects produced is supposed to be<br />
p = 16 ounces with a population standard deviation of o’ = 0.4 ounces. A random<br />
sample of 70 objects yields a mean weight of 15.8 ounces. Is it reasonable to<br />
assume that the production standards are being maintained?<br />
F<br />
11. 1500 randomly selected pine trees were tested for traces of the Bark Beetle<br />
infestation. It was found that 153 of the trees showed such traces. Test the<br />
hypothesis that less than 15% of the Tahoe trees have been infested. (Use a 5%<br />
level of significance)
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