Additional Final Review (Ch.8-10)
When constructing a confidence interval or conducting a hypothesis test, first determine which distribution (normal or t) should be used based on the information that you’re given.
1. What are the similarities and differences of a normal distribution and a t distribution?
Under what circumstances should you use each?
2. A simple random sample is taken in order to obtain a 95% confidence interval for the
population mean. Assuming that the distribution takes on the normal shape, if the
sample size is n = 9, the sample mean is , and the standard deviation of the
sample is s = 6.3, what is the 95% confidence interval?
3. Consider a researcher wishing to estimate the proportion of X-ray machines that
malfunction and produce excess radiation. A random sample of 40 machines is taken
and 12 of the machines malfunction. Construct the 95% confidence interval.
4. A golfer wishes to find a ball that will travel more than 160 yards when hit with his 7-
iron club at a speed of 90 miles per hour. He had a golf equipment lab test a low
compression ball by having a robot swing his club 8 times at the required speed.
The sample resulted in a sample mean of 163.2 yards with a sample standard
deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05
significance level to determine whether the ball meets the golfer’s requirements.
5. An insurance company is reviewing its current policy rates. When originally setting
the rates they believed that the average claim amount was $1,800. They are concerned
that the true mean is actually higher than this, because they could potentially lose a lot
of money. They randomly selected 40 claims, and calculated a sample mean of
$1,950 with a standard deviation of $500. Test to see if the insurance company
should be concerned at the .025 significance level.
6. Trying to encourage people to stop driving to campus, the university claims that on
average it takes people 30 minutes to find a parking space on campus. I don’t think it
takes so long to find a spot. In fact I have a sample of the last five times I drove to
campus, and I calculated the mean time to be 20 minutes. Assuming that the time
it takes to find a parking spot is normal, and that the standard deviation of the sample
is 6 minutes, perform a hypothesis test at the .05 significance level to see if my claim
is correct.
7. Suppose that you interview 1000 exiting voters about who they voted for governor.
Of the 1000 voters, 550 reported that they voted for the democratic candidate. Is
there sufficient evidence to suggest that the democratic candidate will win the
election at the .01 level?
8. In 1990, the average duration of long-distance telephone calls originating in one town
was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis
test to determine whether the average duration of long-distance phone calls has
changed from the 1990 mean of 9.4 minutes. The mean duration for a random sample
of 50 calls originating in the town was 8.6 minutes. Does the data provide sufficient
evidence to conclude that the mean call duration, μ, is different from the 1990 mean
of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of
0.01. Assume that σ = 4.8 minutes.
9. A sample of 10 sales receipts from a grocery store has a mean of $137 and a standard
deviation of $30. Use these values to test whether or not the mean in sales at the
grocery store are different from $150. Test at the .05 significance level.
10. In a quality control situation, the mean weight of objects produced is supposed to be
ounces with a population standard deviation of ounces. A random
sample of 70 objects yields a mean weight of 15.8 ounces. Is it reasonable to
assume that the production standards are being maintained? Test at the .05 level.
11. 1500 randomly selected pine trees were tested for traces of the Bark Beetle
infestation. It was found that 153 of the trees showed such traces. Test the
hypothesis that less than 15% of the Tahoe trees have been infested. (Use a 5%
level of significance)