MAT 209 REVIEW FOR FINAL
In addition to these problems, review all previous tests.
1. The following table shows the percentages of the vote predicted by a poll for 6
candidates in different states X, and the corresponding percentages of the vote
that they actually received, Y:
X (Poll)
55
40
53
41
59
34
Y (Election)
57
37
59
43
55
33
Calculate the coefficient of correlation, r for these data. Test the significance of the value
of r at the level of significance 0.01
2. Fit a least squares line (best fit line) to the data in question 2, and use it to predict the
value of Y when X = 50
3. Women’s weights are normally distributed with a mean of 143 lbs and a standard
deviation of 29 lbs. If a woman is randomly selected, find the probability that her weight
is greater than 150 lbs. Is a continuity correction necessary? Explain.
4. If a student answers 40 multiple choice questions, each with four possible answers, by
guessing randomly, use the normal approximation to the binomial to find the probability
that she answers at least 15 correctly.
5. If the mean of a random sample of size 81 is used to estimate the mean of a population
with σ = 18, what is the probability that the error is less than 3, based on the central limit
theorem?
6. Suppose we use the mean of a random sample of size n = 49 to estimate the mean of a
population with σ = 28. Use Chebyshev’s theorem to compute the probability that the
error is less than 12.
7. Assume that women’s heights are normally distributed with a mean given by  = 63.6
in and a standard deviation given by  = 2.5 in. If 100 women are randomly selected,
use the central limit theorem to find the probability that they have a mean height
between 63.5 inches and 64 inches.
8. A manufacturer of light bulbs claims that its light bulbs have a mean life of 1520 hrs
with standard deviation of 85 hr. A random sample of 40 such light bulbs is
selected for testing. If the sample produces a mean value of 1498.3 hr, is there
sufficient evidence to claim that the mean life is less than the manufacturer claimed?
Use significance level,  = 0.01.
9. A physician claims that joggers’ maximal volume uptake is greater than the average
for all adults. A sample of 15 joggers has a mean of 40.6 milliliters per kilogram (ml/kg)
and a standard deviation of 6 ml/kg. If the average of all adults is 36.7 ml/kg, is there
enough evidence to support the physician’s claim? Use significance level,  = 0.05.
10. A job placement director claims that the average starting salary for nurses is $24,000.
A sample of 10 nurses has a mean of $23,450 and a standard deviation of $400. Is there
enough evidence to reject the director’s claim in favor of the alternative that the mean is
less than $24,000. Use significance level,  = 0.05.
11. Page 441 # 13.4 (one sample sign test)
12. Page 441 # 13.5 (paired sample sign test)