Download MTH 1431: Introduction to Statistics Final Exam Review

MTH 1431: Introduction to Statistics
Final Exam Review- Focus studying on these topics.
Your exam will consist of roughly 33 multiple choice questions.
1. Classify the following variables as qualitative or quantitative. If the variable is quantitative, state whether it is
discrete or continuous.
a. Species of tree sold at a nursery
b. Wait time at a amusement park ride
c. Frequency with which the word “the” appears in a selection of prose
d. Brand name of a pair of jeans
2. State whether the following depicts an observational study or an experiment.
a. A sample of registered voters is asked, “Do you agree with the president’s health care proposal?”
b. A sample of 10 Chevy trucks is divided into two groups. In the first group 5W-30 motor oil is used, and
in the second 10W-30 motor oil is used. All other variables are controlled and the average MPG is
measured. The two groups are compared.
c. On an election day, a pollster for Fox News is positioned outside of a polling place near her home. She
asks the first 50 voters leaving the facility to complete a survey.
3. The following data represent the pulse rate of eight randomly selected females after stepping up and down on a
6-inch platform for 3 minutes. Pulse is measured in beats per minute.
136, 169, 120, 128, 129, 143, 115, 146, 96, 86
a. Find the sample mean and median pulse rate.
b. Find the sample standard deviation and variance.
c. Find Q1, Q3, and the interquartile range.
4. Find the area under the standard normal curve between z = -2 and z = 1.
5. Find the area under the standard normal curve between z = -0.75 and z = 1.3.
6. For a normal distribution, find P(1 < z < 1.8).
7. Suppose that test scores are normally distributed with µ=80 and σ=8. Find the probability that a randomly
selected student will score between 75 and 88 on the test.
8. What is the probability of rolling a 2 on a (fair, six-sided) die? What is the probability of rolling a 2 or a 4 on the
die? Of rolling more than 2 on the die?
9. A bag of 30 tulip bulbs purchased from a nursery contains 12 red tulip bulbs, 10 yellow bulbs, and 8 purple tulip
bulbs. What is the probability that a randomly selected bulb will be red or yellow?
10. A sample of size n = 10 is taken from a normal distribution with µ=100 and σ=10.
a. What is the probability that the sample mean will be greater than 105?
b. What is the probability that the sample mean will be less than 100?
c. What is the probability that the sample mean will be between 102 and 105?
11. Given
, construct a 95% confidence interval for µ.
12. Given
, construct a 90% confidence interval for µ.
13. Given the 90% confidence interval, (22.25, 26.15), how sure are you that µ= 28?
14. What is the effect of increasing the level of confidence on the width of the interval?
15. In a study of aerobic activity, the blood plasma volume (in liters) of 12 women was measured, and following data
were obtained:
3.15, 2.99, 2.77, 3.12, 2.45, 3.85, 2.99, 3.87, 4.06, 2.94, 3.53, 3.21
a. Use the data to compute a point estimate for the population mean.
b. Suppose that the data does not contain any outliers and the blood plasma volume is normally
distributed. Construct a 95% confidence interval for the mean blood plasma level.
c. Interpret the interval in part b.
d. Construct a 99% confidence interval for the mean blood plasma level.
16. Given: Ho: µ = 100 versus H1: µ<100, if we reject Ho, what does this mean? If we fail to reject Ho, what does this
mean?
17. To test Ho: µ = 3.9 versus H1: µ < 3.9, a simple random sample of size n = 25 is obtained from a population that is
known to be normally distributed.
compute the test statistic.
a. If
b. If the researcher decides to test the hypothesis at the α= 0.05 level of significance, determine the critical
value.
c. Will the researcher reject the null hypothesis?
d. Determine the p-value.
18. Given Ho: µ = 59 versus Ha: µ ≠59, α= 0.01 and p-value = 0.0234, what decision should be made?
19. A nutritionist thinks that 20-29 year old females consume too much sodium and a test of significance is
conducted.
a. Interpret what a Type I error would mean in this setting.
b. What would a Type II error mean?
20. For the following, assume that the populations are normally distributed and that independent sampling has
occurred.
Population 1: n = 13, = 32.4, s = 4.5
Population 2: n = 8, = 28.2, s = 3.8
a. Compute the test statistic for Ho: µ1= µ2 versus H1: µ1≠ µ2.
b. If α=0.05, what decision will be made?
c. Compute a 95% confidence interval for µ1 - µ2.
21. Compute the test statistic for Ho: µ = 59 versus Ha: µ ≠59, if = 61, σ= 12, and n = 35.
22. It was reported 35% of families eat dinner together as a family seven days per week. A recent poll shows that
128 out of 400 families ate dinner together 7 days per week during the last month. We wish to test whether the
sample data gives us evidence to conclude that the proportion of families who eat dinner together 7 days per
week is different from 0.35.
a.
b.
c.
d.
e.
State the hypotheses for a test of significance in this situation.
State the sample statistic.
Compute the test statistic and p-value.
Interpret your results.
Compute a confidence interval for p, the true proportion of families who eat together.
23. If I take a random sample of size 40 from a skewed population, what can be said about the sampling distribution
of sample means? When are inference procedures valid when sampling from skewed population distributions?
When do we use t-procedures? z-procedures?
24.
Student
Nine students took the SAT. Their scores are listed below. Later on, they read a book on test preparation and
retook the SAT. Their new scores are listed below. Construct a 95% confidence interval for µd (the true mean
difference in scores). Assume that the distribution is normally distributed.
Scores
before prep
book
Scores
after prep
book
25.
1
720
2
860
3
850
4
880
5
860
6
710
7
850
8
1200
9
950
740
860
840
920
890
720
840
1240
970
Many track hurdlers believe that they have a better chance of winning if they start in the inside lane that is
closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on
until the outermost lane, Lane 6. The data lists the number of wins for track hurdlers in the different starting
positions. Calculate the chi-square test statistic χ2 to test the claim that the probabilities of winning are the
same in the different positions. Use α = 0.05. The results are based on 240 wins.
Starting Position
Number of Wins
1
50
2
36
3
45
4
44
5
32
6
33