Math 3339 Online
Review for Final Exam
1. (Assuming a set has all positive values) If the largest value of a data set is doubled,
which of the following is not true?
a. The mean increases.
b. The standard deviation increases.
c. The interquartile range increases.
d. The range increases.
2. A potato chip company calculated that there is a mean of 74.1 broken potato chips in
each production run with a standard deviation of 5.2. If the distribution is
approximately normal, find the probability that there will be fewer than 60 broken chips
in a run.
3. What does it mean if the correlation coefficient, r, is close to 1? is close to 0?
4. In the regression equation y = b0 + b1x, identify what b0 and b1 represent. Which of
these will best explain the relationship between x and y?
5. Be able to identify type I and type II errors from an example.
6. It is fourth down and a yard to go for a first down in an important football game. The
football coach must decide whether to go for the first down or punt the ball away. The
null hypothesis is that the team will not get the first down if they go for it. The coach
will make a Type I error by doing what?
a. Deciding not to go for the first down when his team will get the first down.
b. Deciding not to go for the first down when his team will not get the first down.
c. Deciding to go for the first down when his team will get the first down.
d. Deciding to go for the first down when his team will not get the first down.
e. None of the above.
7. The following table displays the results of a sample of 100 in which the subjects
indicated their favorite ice cream of three listed. The data are organized by favorite ice
cream and age group. What is the probability that a person chosen at random will be
over 40 if he or she favors chocolate?
Age Chocolate Vanilla Strawberry
Over 40 15 8 7
20 – 40 20 11 15
Under 20 8 7 9
, 8. A random variable X has a probability distribution as follows:
X 0 1 2 3
P(X) 4k 5k 8k 3k
Find the probability that P(X < 2.0)
9. The amount of time it takes a bat to eat a frog was recorded for each bat in a random
sample of 12 bats. The resulting sample mean and standard deviation were 21.9 minutes
and 7.7 minutes, respectively. Assuming it is reasonable to believe that the population
distribution of bat mealtimes of frogs is approximately normal,
a. Construct a 95% confidence interval for the mean time for a bat to eat a frog.
b. Construct a 95% confidence interval for the variance of the time for a bat to eat
a frog.
10. Suppose that the average weekly grocery bill for a family of four is $140 with a
standard deviation of $10. If the next 52 weeks can be viewed as a random sample from
a population with this center and spread, then the approximate probability that the total
grocery bill for one year is less than $7020 is 0.0002. This problem can also be solved
using the sampling distribution of the sample average. Complete probability statement.
⎛ ⎞
P⎜ Z < ⎟⎠
⎝
11. One of your peers claims that boys do better in math classes than girls. Together you
run two independent simple random samples and calculate the given summary statistics
of the boys and the girls for comparable math classes. In Calculus, 15 boys had a mean
percentage of 82.3 with standard deviation of 5.6 while 12 girls had a mean percentage
of 81.2 with standard deviation of 6.7. Which of the following would be the most
appropriate test for establishing whether boys do better in math classes than girls?
a. two-sample z-test for means
b. two-sample t-test for means
c. chi-square test
d. two-sample z-test for proportions
e. none of these tests would be appropriate
12. Rainwater was collected in water collectors at thirty different sites near an industrial
basin and the amount of acidity (pH level) was measured. The mean and standard
deviation of the values are 4.60 and 1.10 respectively. When the pH meter was
recalibrated back at the laboratory, it was found to be in error. The error can be
corrected by adding 0.1 pH units to all of the values and then multiply the result by 1.2.
Find the mean and standard deviation of the corrected pH measurements.
13. What is the expected value and the variance of the discrete probability function given in
the table below?
Outcome 1 2 3 4 5 6
Probability .1 .2 .3 .3 0 .1
Review for Final Exam
1. (Assuming a set has all positive values) If the largest value of a data set is doubled,
which of the following is not true?
a. The mean increases.
b. The standard deviation increases.
c. The interquartile range increases.
d. The range increases.
2. A potato chip company calculated that there is a mean of 74.1 broken potato chips in
each production run with a standard deviation of 5.2. If the distribution is
approximately normal, find the probability that there will be fewer than 60 broken chips
in a run.
3. What does it mean if the correlation coefficient, r, is close to 1? is close to 0?
4. In the regression equation y = b0 + b1x, identify what b0 and b1 represent. Which of
these will best explain the relationship between x and y?
5. Be able to identify type I and type II errors from an example.
6. It is fourth down and a yard to go for a first down in an important football game. The
football coach must decide whether to go for the first down or punt the ball away. The
null hypothesis is that the team will not get the first down if they go for it. The coach
will make a Type I error by doing what?
a. Deciding not to go for the first down when his team will get the first down.
b. Deciding not to go for the first down when his team will not get the first down.
c. Deciding to go for the first down when his team will get the first down.
d. Deciding to go for the first down when his team will not get the first down.
e. None of the above.
7. The following table displays the results of a sample of 100 in which the subjects
indicated their favorite ice cream of three listed. The data are organized by favorite ice
cream and age group. What is the probability that a person chosen at random will be
over 40 if he or she favors chocolate?
Age Chocolate Vanilla Strawberry
Over 40 15 8 7
20 – 40 20 11 15
Under 20 8 7 9
, 8. A random variable X has a probability distribution as follows:
X 0 1 2 3
P(X) 4k 5k 8k 3k
Find the probability that P(X < 2.0)
9. The amount of time it takes a bat to eat a frog was recorded for each bat in a random
sample of 12 bats. The resulting sample mean and standard deviation were 21.9 minutes
and 7.7 minutes, respectively. Assuming it is reasonable to believe that the population
distribution of bat mealtimes of frogs is approximately normal,
a. Construct a 95% confidence interval for the mean time for a bat to eat a frog.
b. Construct a 95% confidence interval for the variance of the time for a bat to eat
a frog.
10. Suppose that the average weekly grocery bill for a family of four is $140 with a
standard deviation of $10. If the next 52 weeks can be viewed as a random sample from
a population with this center and spread, then the approximate probability that the total
grocery bill for one year is less than $7020 is 0.0002. This problem can also be solved
using the sampling distribution of the sample average. Complete probability statement.
⎛ ⎞
P⎜ Z < ⎟⎠
⎝
11. One of your peers claims that boys do better in math classes than girls. Together you
run two independent simple random samples and calculate the given summary statistics
of the boys and the girls for comparable math classes. In Calculus, 15 boys had a mean
percentage of 82.3 with standard deviation of 5.6 while 12 girls had a mean percentage
of 81.2 with standard deviation of 6.7. Which of the following would be the most
appropriate test for establishing whether boys do better in math classes than girls?
a. two-sample z-test for means
b. two-sample t-test for means
c. chi-square test
d. two-sample z-test for proportions
e. none of these tests would be appropriate
12. Rainwater was collected in water collectors at thirty different sites near an industrial
basin and the amount of acidity (pH level) was measured. The mean and standard
deviation of the values are 4.60 and 1.10 respectively. When the pH meter was
recalibrated back at the laboratory, it was found to be in error. The error can be
corrected by adding 0.1 pH units to all of the values and then multiply the result by 1.2.
Find the mean and standard deviation of the corrected pH measurements.
13. What is the expected value and the variance of the discrete probability function given in
the table below?
Outcome 1 2 3 4 5 6
Probability .1 .2 .3 .3 0 .1
