Download Review Midterm 1 Stat 212 Question 1 : Find the sample mean

Review Midterm 1
Stat 212
Question 1 :
Find the sample mean, median, variance, and standard deviation for the following data.
(Show your work!)
4
Mean = (4+3+8+4+1)/5= 4
xi
Total
3
4
Variance = 26/4 = 6.5
xi-mean
4
3
8
4
1
20
8
1
S= Sqrt(Variance) = 2.54951
(xi-mean)^2
0
-1
4
0
-3
0
0
1
16
0
9
26
Question 2 :
a) Baseball player Joe Slabotnik has had thirty hits in one hundred chances so far this season.
Therefore has a batting average of 30/100 = .300, i.e., a probability of .300 of getting a
hit. This is an example of which approach to probability?
classical
frequentist
subjective
b) Based upon a survey of 1600 California residents, Gallup Poll notes that, if the election were
held today, over half of all voters would vote to recall Gov. Davis. This is an example of
probability
descriptive statistics
inferential statistics
c) Average SAT score among all students at the University of Southern North Dakota at Hoople
is 942. This is an example of
probability
descriptive statistics
inferential statistics
Question 3. Suppose that the probability of the event A is 0.32, the probability of the event B is
0.38, while the probability of their union (A or B) is 0.70. Are the events A and B mutually
exclusive? Explain your answer.
A. Yes Because P(A or B ) = P(A) + P(B), so P(A and B) = 0
B. No
Question 4. A grocery store employs cashiers, stock clerks and deli personnel. The distribution
of employees according to marital status is shown below. If employees is selected at random,
find these probabilities
Cashiers
Married
Not Married
Total
8
5
Stock Clerks
Deli Personnel
12
3
15
2
13
27
5
23
22
45
(a) The employee is a stock clerk or married (27+23-12)/45 = 38/45
(b) The employee is not married 22/45
(c) The employee is a cashier or is not married
(13+22-5)/45 = 30/45
(d) The employee is a cashier and deli personnel 0
(e) The employee is a cashier or deli personnel (13+5)/45 = 18/45
(f) Find the probability that the employee is a cashier given that he/she is married 8/23
(g) Are the events “employee is not married” and “employee is a stock clerk” independent?
No, because P(Not Married and a Stock Clerk) does not equal to P(Not Married) * P(Stock
Clerk)
Question 5.
18-21
21-30
30-45
>= 45
Revenue source
Liquor
Gambling stores
Other
33
68
12
55
121
50
117
109
132
158
110
90
18-21
21-30
30-45
>=45
Total
Gambling Liquor
Other
Total
33
68
12
113
55
121
50
226
117
109
132
358
158
110
90
358
363
408
284
1055
a. P(Gambling) 363/1055
b. P(30-45/Liquor) 109/408
c. P(Other/18-21) 12/113
d. P(21-30/Gambling) 55/363
e. P(18-21 or >=45) (113+358)/1055 = 471/1055
Question 6. A corporation has three methods of training employees. Because of time, space, and
location, it sends 20% of its employees to location A, 35% to location B, and 45% to location C.
Location A has an 80% success rate. That is 80% of the employees who complete the course will
pass the licensing exam. Location B has a 75% success rate, and location C has a 60% success
rate. If a person has passed the exam, find the probability that the person went to location B.
P(A) = 0.2
P(B) = 0.35
P(C) = 0.45
Let S is the success rate
P(S/A) = 0.8
P(S/B) = .75
P(S/C) = .6
P(S and A) = P(S/A) * P (A) = 0.16
P(S and B) = P(S/B) * P(B) = 0.2625
P(S and C) = P(S/C) *P(C) = 0.27
P(S) = P(S and A) + P(S and B) + P (S and C) = 0.6925
P(B/S) = P (B and S) / P(S) = 0.2625 / 0.6925 = 0.379061
A
S
NS
Total
B
0.16
0.04
0.2
C
0.2625
0.0875
0.35
Total
0.27
0.6925
0.18
0.3075
0.45
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Question 7. There are three children in the Stribling family.
(B,B,B) (B,G,G) (B,G,B) (B,B,G) (G,G,G) (G,G,B) (G,B,B) (G,B,G)
a. Determine the probability that all the children are girls 1/8
b. Determine the probability that at least one children are boys 7/8
c. Determine the probability that exactly two children are boys 3/8
d. Determine the probability that exactly two children are girls 3/8
Question 8.
Grade
Studying Hours per week (x) (y)
2
50
4
60
6
70
8
90
10
95
a. Calculate the Pearson correlation coefficient
0.998
b. Determine equation of least squares line that can be used for predicting a value of y based
on a value of x
Y_hat = 37.43 + 5.73 x_hat
c. Compute SSE for the least squares line 5.69
d. Calculate R2
0.996
e. Use your prediction equation to predict grade with the studying hours is 7 hours
77.54
Question 9. In past studies, it has been found that the distribution of weights for a certain
population of young men ages 21 to 29 is normal with mean 180 pounds and standard deviation
25 pounds
a. Given these facts, what proportion of this population weights more than 200 pounds
Z = (200-18)/25 = 0.8 … Look at the z (normal) table (positive z)
P(X > 200) = 1 – P (X<200) = 1 – P (Z < 0.8) = 1 – 0.7881 = 0.2119
b. Given these facts, what proportion of this population weights less than 170 pounds
Z = (170-180)/25 = - 0.4 … Look at the normal table (negative z)
P (X < 170) = P (Z < - 0.4) = 0.3446
c. Given these facts, what proportion of this population weights between 170 and 200
pounds
P ( X < 200) – P (X<170) = 0.4435
P (X < 200) = 0.7881
P (X < 170) = 0.3446
Question 10. Given the following set of numbers:
X = {7.1 1.8 2.1 1.5 2.1}
a. Calculate the mean, median and mode 2.92 2.1 2.1
b. Change the largest observation in the data set to 4.3 and calculate the mean and median
for the new data set 2.36 2.1 2.1
c. Comparing the results of part a and part b, what do you learn about the median and the
mean?
Median is resistant
Question 11. Two fair dice are tossed. Find the probability that their sum is less than 6
1
2
3
4
5
6
1
2
3
4
5
6
7
2
3
4
5
6
7
8
3
4
5
6
7
8
9
4
5
6
7
8
9
10
5
6
7
8
9
10
11
6
7
8
9
10
11
12
10
10/36
Question 12. In regression analysis, if the coefficient of determination (R2) is 1.0, then:
a.
b.
c.
d.
SSE (error sum of squares) must be 1.0
SSE must be 0.0
No Linear Relationship
X and Y are independent
Perfect Linear Relationship ----- > no error (residual) or the predicted Y and the actual Y are the
same, so the different between the actual Y and predicted Y is 0
Question 13. What do residuals represent in the simple linear regression model?
a. The different between the actual Y values and the mean of Y
b. The different between the actual Y values and the predicted Y values
c. The square root of the slope
d. The predicted value of Y for the average X value
e. None of the above
Question 14. An elevator serving a hospital is designed to hold up 15 passages and has a
maximum safe capacity of 2440 pounds. The weight of passengers who use the elevator is
normally-distributed with an average of 149 pounds and a standard deviation of 20 pounds
a. What is the probability that a single passenger on the elevator weights between 140 and
150 pounds?
P(X < 150) – P(X<140) = .1935
Z = (150-149)/20 = 0.05
P(X<150) = .5199
Z = (140 – 149)/20 = -.45
P(X<140) = .3264
b. What is the probability that a single passenger on the elevator weights more than 200
pounds?
P(X > 200) = 1 – P(X<200) = 0.0054
Z = (200-149)/20 = 2.55
P (X < 200) = 0.9946
Question 15. Which the following variables are described as a Quantitative data:
a.
b.
c.
d.
Hair Color
Gender
Number of children in a family
Marital Status
Question 16. Find the relative Frequency
Marital Status
Never married
Married
Widowed
Divorced
Total
Frequency
55.3
127.7
13.9
22.8
219.7
Relative Frequency
0.251707
0.581247
0.063268
0.103778
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