MATH 3070: Sample questions for final exam

MATH 3070: Sample questions for final exam
Question 1. Find the median for the given sample data.
1) The temperatures (in degrees Fahrenheit) in 7 different cities on New Year's
Day are listed below. Find the median temperature.
29
67
68
78
33
59 26
Question 2. Find the z-score corresponding to the given value and use the z-score
to determine whether the value is unusual.
2) The systolic blood pressure of 18-year-old women is normally distributed
with a mean of 120 mmHg and a standard deviation of 12 mmHg. An 18year-old woman have a systolic blood pressure of 140 mmHg. Is it unusual?
3) A body temperature of 99.5° F given that human body temperatures have a
mean of 98.2° F and a standard deviation of 0.6°. Is it unusual?
Question 3. Find the mean, μ, for the binomial distribution which has the stated
values of n and p.
4) n = 40; p = 3/5
Question 4. In a clinical trial, 800 subjects were treated with a drug, and 34 subjects
experienced nausea. The probability of nausea for subjects not receiving the
treatment was 0.02.
5) Assuming that the drug has no side effect, and that the probability of nausea
is 0.02, find the mean for the number of people in the group of 800 who can
be expected to experience nausea. Hint: How do you find the answer in
Question 3?
6) The standard deviation 4 was also calculated. Is it unusual to find that
among 800 people there are 34 who experience nausea? Why or why not?
Hint: How do you find the answers in Question 2?
7) Based on the preceding results, does nausea appear to be an adverse
reaction that should be of concern? Justify your answer. Hint: Can you still
believe that the proportion of subjects experiencing nausea remains the same when
they are treated with a drug?
Question 5. If z is a standard normal variable, find the probability, or the critical
value.
8) The probability that z is less than 1.13
9) P(z > 0.59)
10) z0.005
Question 6. Find the z score, or the probability.
11) IQ scores of adults are normally distributed with a mean of 100 and a
standard deviation of 15. Find the z score to the IQ score of 90.
12) Assume that adults have IQ scores that are normally distributed with a mean
of 100 and a standard deviation of 15. Find the probability that a randomly
selected adult has an IQ between 90 and 120.
Question 7. Find the standard deviation, or the probability.
13) The annual precipitation amounts in a certain mountain range is normally
distributed with a mean of 107 inches, and a standard deviation of 12 inches.
What is the standard deviation for the average annual precipitation during
36 randomly picked years?
14) The annual precipitation amounts in a certain mountain range are normally
distributed with a mean of 107 inches, and a standard deviation of 12
inches. What is the probability that the average annual precipitation during
36 randomly picked years will be less than 109.8 inches?
Question 8. Interpret the result of study.
15) Randomly selected students participated in an experiment to test their ability
to determine when sixty seconds has passed. Forty students yielded a sample
mean of 61.1 seconds, and a 95% confidence interval 58 < μ < 64.2 was
obtained. Based on the result is it likely that the students' estimates have a
mean that is reasonably close to sixty seconds? Why or why not?
16) A physician wants to determine whether there are significant differences in
pulse rate between males and females, and obtained a 95% confidence
interval 61.3 < μ < 78.7 for the mean pulse rate for males, and a 95%
confidence interval 75.5 < μ < 101.3 for the mean pulse rate for females. Can
we conclude that the population means for males and females are different?
Why or why not?
Question 9. Express the null hypothesis H 0 and the alternative hypothesis H A
in symbolic form.
17) Carter Motor Company claims that its new sedan, the Libra, will average
better than 26 miles per gallon in the city. Use μ, the true average mileage of
the Libra.
Question 10. Formulate the indicated conclusion in nontechnical terms. Be sure to
answer whether you can support the original claim or not.
18) An entomologist writes an article in a scientific journal which claims that
fewer than 12 in ten thousand male fireflies are unable to produce light due
to a genetic mutation. Assuming that a hypothesis test of the claim has been
conducted and that the conclusion is to reject the null hypothesis, state the
conclusion in nontechnical terms.
Question 11. Express the confidence interval using the indicated format.
19) Express the confidence interval 0.66 < p < 0.8 in the form of ± E.
Question 12. Do one of the following, as appropriate: (a) Find the critical value
, or (b) find the critical value
.
20) (1-α) = 90%; n = 10; σ is unknown; population appears to be normally
distributed.
Question 13. The College Board Exams are administered each year to many thousands of
high school students, and are scored so as to yield a mean of 500 and a standard deviation of
100. The distribution of the scores is close to a normal distribution.
21)
What percentage of the scores can be expected to be less than 432.
22)
What percentage of the scores can be expected to be greater than 645.
Question 14. A random sample of 25 investment plans shows the sample mean 3.8% and
the sample standard deviation 5% for their annual yield. The annual yield of various
investment plans has a normal distribution.
23)
Find a 95% confidence interval the average annual yield of the investment.
24) If the margin of error for the 95% confidence interval must be less than 0.98
percentage points, how large the size of a random sample is required? Use the current
estimates with the critical value z0.025 = 1.96.
Question 15. The chemistry lab manual says “your own experiment should conclude with
significance level 0.05 that the population mean is greater than 4.2. In the experiment you
are supposed to make 40 measurements.”
25) Write the null hypothesis H 0 and the alternative hypothesis H A in symbolic
form regarding the true population mean μ .
26)
Suppose that we obtain the test statistic T =1.52 and the critical value 1.685. What
do you say about the null hypothesis?
27)
Explain what “Type II error” is, and when it happens.
28)
Continue from the previous question. If the p-value is 0.068, what would you
conclude in your lab report?
Question 16. In making aluminum castings, an average of 3.5 ounces per casting is trimmed
off and recycled as a raw material. A new manufacturing process has been proposed to
reduce the amount of aluminum that must be recycled in this way. The data were collected
from the new process, and the QQ plot are shown below.
29)
To test whether the new process reduces the amount of trimmed aluminum, state the
null hypothesis H 0 and the alternative hypothesis H A using the population mean
μ of trimmed aluminum.
30)
Is it reasonable to assume that the data come from a normal distribution? Why or
why not?
31)
The p-value 0.11 is obtained. Choose the significance level, and write your own
conclusion on whether the new process reduces the amount of trimmed aluminum.
32) Do you recommend the future study? If so, what do you suggest for the next
experiment?