Final Exam Review Questions Solutions Guide
MATH 399 Statistics
Final Exam
Review Questions
Solutions Guide
You may want to PRINT THIS so you can carefully check your answers. Be sure to ask
your instructor if you have questions about any of the solutions given below.
1. Determine if each of the following represents nominal, ordinal, interval, or ratio data.
a. Movie ratings
b. Test scores
c. Colors of shirts
Solution: (a) ordinal data since movie ratings have an order, but cannot be subtracted; (b) ratio
data since there is a real zero; (c) nominal data as there is not even order to these data.
2. The following numbers represent the weights in pounds of six 7- year old children in Mrs.
Jones' 2nd grade class.
{25, 60, 51, 47, 49, 45}
Find the mean; median; mode; range; variance; standard deviation.
Solution: mean = 46.17
median = 48
mode does not exist range = 35.00
variance = 134.57
standard deviation =11.60
3. If the variance is 846, what is the standard deviation?
Solution: standard deviation = square root of variance = sqrt(846) =
29.086
4. If we have the following data
34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66
Draw a stem and leaf. Discuss the shape of the distribution.
Solution:
2|219200
3|48714
4|0197
, Final Exam Review Questions Solutions Guide
MATH 399 Statistics
5|
6|6
This distribution is right skewed (positively skewed) because the “tail”
extends to the right.
5. What type of sampling technique is (a) a wheat field is divided into sections and a random
sample of stocks are taken from each section, and (b) a manufacturer measures every 80th
bottle to test for quality?
Solution: (a) stratified sample as dividing into sections and sampling the same number from
each section is a stratified sample and (b) systematic as there is a system to how the sample is
being selected.
6. If a data set with a normal distribution has a mean of 32 and a standard deviation of 4.9,
what percent of the data would you expect to find between 27.1 and 36.9? What range
encompasses 99.7% of these data?
Solution: Based on the empirical rule, about 68% of the data would be within that range as 32-
4.9 = 27.1 and 32+4.9=36.9. The range to include 99.7% of the data would be within 3 standard
deviations of the mean which would be 32-3(4.9)=17.3 and 32+3(4.9)=46.7.
7. Determine the regression equation for the following data:
X: 4 5 7 3 2 7 8 9 7 6 4 6 5 9 3 2 1
Y: 9 7 8 6 9 5 6 4 3 6 7 8 9 3 4 2 4
Solution: y^ = 6.442 – 0.108x
8. If the correlation coefficient is -.749, what would be the value of the coefficient of
determination?
Solution: The coefficient of determination is (-0.749)2 = 0.561.
9. To predict the annual rice yield in pounds we use the equation
yˆ = 859 + 5.76x1 + 3.82x2 , where x1 represents the number of acres planted and where x2
2
represents the number of acres harvested and where r = .94.
a) Predict the annual yield when 3200 acres are planted and 3000 are harvested.
2
b) Interpret the results of this r value.
Solution:
(a) yˆ = 859 + 5.76*3200 + 3.82*3000
= 859 + 18432 + 11460
= 30751 which is 30,751 pounds of rice
MATH 399 Statistics
Final Exam
Review Questions
Solutions Guide
You may want to PRINT THIS so you can carefully check your answers. Be sure to ask
your instructor if you have questions about any of the solutions given below.
1. Determine if each of the following represents nominal, ordinal, interval, or ratio data.
a. Movie ratings
b. Test scores
c. Colors of shirts
Solution: (a) ordinal data since movie ratings have an order, but cannot be subtracted; (b) ratio
data since there is a real zero; (c) nominal data as there is not even order to these data.
2. The following numbers represent the weights in pounds of six 7- year old children in Mrs.
Jones' 2nd grade class.
{25, 60, 51, 47, 49, 45}
Find the mean; median; mode; range; variance; standard deviation.
Solution: mean = 46.17
median = 48
mode does not exist range = 35.00
variance = 134.57
standard deviation =11.60
3. If the variance is 846, what is the standard deviation?
Solution: standard deviation = square root of variance = sqrt(846) =
29.086
4. If we have the following data
34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66
Draw a stem and leaf. Discuss the shape of the distribution.
Solution:
2|219200
3|48714
4|0197
, Final Exam Review Questions Solutions Guide
MATH 399 Statistics
5|
6|6
This distribution is right skewed (positively skewed) because the “tail”
extends to the right.
5. What type of sampling technique is (a) a wheat field is divided into sections and a random
sample of stocks are taken from each section, and (b) a manufacturer measures every 80th
bottle to test for quality?
Solution: (a) stratified sample as dividing into sections and sampling the same number from
each section is a stratified sample and (b) systematic as there is a system to how the sample is
being selected.
6. If a data set with a normal distribution has a mean of 32 and a standard deviation of 4.9,
what percent of the data would you expect to find between 27.1 and 36.9? What range
encompasses 99.7% of these data?
Solution: Based on the empirical rule, about 68% of the data would be within that range as 32-
4.9 = 27.1 and 32+4.9=36.9. The range to include 99.7% of the data would be within 3 standard
deviations of the mean which would be 32-3(4.9)=17.3 and 32+3(4.9)=46.7.
7. Determine the regression equation for the following data:
X: 4 5 7 3 2 7 8 9 7 6 4 6 5 9 3 2 1
Y: 9 7 8 6 9 5 6 4 3 6 7 8 9 3 4 2 4
Solution: y^ = 6.442 – 0.108x
8. If the correlation coefficient is -.749, what would be the value of the coefficient of
determination?
Solution: The coefficient of determination is (-0.749)2 = 0.561.
9. To predict the annual rice yield in pounds we use the equation
yˆ = 859 + 5.76x1 + 3.82x2 , where x1 represents the number of acres planted and where x2
2
represents the number of acres harvested and where r = .94.
a) Predict the annual yield when 3200 acres are planted and 3000 are harvested.
2
b) Interpret the results of this r value.
Solution:
(a) yˆ = 859 + 5.76*3200 + 3.82*3000
= 859 + 18432 + 11460
= 30751 which is 30,751 pounds of rice
