Download MA155 Statistical Reasoning

MA155 Statistical Reasoning
Test (3.1 to 3.4, 4.1 to 4.3)
100 pts.
MULTIPLE CHOICE—Circle the correct answer. (3 pts each)
1.
Name_______________________________
The following figures give the distribution of land (in acres) for a county containing 88,000 acres. Which graph
represents the correct pie chart?
Use the following information and graph to answer #2-3.
2.
In the year 1990, approximately what percentage of Danny’s
total investment was in the CD?
a. 15%
b. 20%
c. 25%
d. 30%
3.
In the year 1998, what was the approximate value of Danny’s
investment in mutual funds?
a. $4000
b. $2500
c. $1900
d. $6000
Use the following information and graph to answer #4.
4.
Given that 600 people were aged between 25 and 40, approximately
how many had a systolic blood pressure reading between 100 and 119?
a. 50
b. 30
c. 300
d. 500
5. Identify the distribution as symmetric, left-skewed or right-skewed.
The birth weight of healthy babies born in 2009 at Southeast Hospital.
a. Right-skewed
b. Left-skewed
c. Symmetric
6.
Identify the distribution as symmetric, left-skewed or right-skewed. Number of days worked last year by adult
males in a U.S. city which has a low unemployment rate.
a. Right-skewed
b. Left-skewed
c. Symmetric
FREE RESPONSE—Be sure to completely answer each question.
7. A medical research team studied the ages of patients who had strokes caused by stress. The ages of 34 patients
who suffered stress strokes is indicated by the binned frequency table below.
a. Construct a histogram using the table. Be sure to label axes correctly. (7 pts.)
8.
b.
What bin represents the modal age that a patient has a stroke caused by stress? (3 pts.)
c.
What bin represents the median age that a patient has a stroke caused by stress? (3 pts.)
A frequency table for the number of persons with various blood types is indicated below.
a. Complete the relative frequency column for the data. Give your answers correct to the nearest tenth of a
percent. (6 pts.)
Blood Type Frequency Relative Frequency
O
19
b.
A
13
B
5
AB
3
What type of graph would you use to best represent this data? Explain why. (4 pts.)
9.
Calculate the standard deviation for the data set: 5, 5, 6, 8. Show work using the formula: 𝑠 = √
(5 pts.)
10. The midterm test scores for a class are listed below.
85 77 93 91 74 65 68 97 88 59 74 83 85 72 63 79
a. Construct a stemplot of the data. (7 pts.)
b.
Find the mean of the data. (4 pts.)
c. Find the five-number summary. Be sure to label each number appropriately. (6 pts.)
d.
Draw a boxplot. Be sure to use an appropriate scale. (6 pts.)
e.
Discuss the shape of the distribution. (4 pts.)
∑(𝑥−𝑥̅ )2
𝑛−1
11. Suppose that after 50 at-bats a baseball player has a batting average of 0.400. If the baseball player gets a hit in
the next at-bat, what will the player’s new batting average be? (The batting average is the number of hits
divided by the number of at-bats.) (6 pts.)
12. Joe orders take-out from a specific Chinese restaurant on a regular basis. After many weeks of collecting data,
he determines the restaurant has a mean delivery time of 25 minutes with a standard deviation of 10 minutes.
One day it takes him 40 minutes to receive his order. Is his order “unusually” late? Explain using the mean and
standard deviation. (6 pts.)
13. Dave is a college student contemplating a possible career option. One factor that will influence his decision is
the amount of money he is likely to make. He decides to look up the average starting salary of graduates in that
profession. Which information would be most useful to him, the mean starting salary or the median starting
salary? Why? (5 pts.)
14. Explain how two data sets could have equal means and modes but still differ greatly. Give an example with two
data sets to illustrate. (5 pts.)
15. The host of a dinner party purchases wine based on the weighted average of clarity (10%), bouquet (3%),
friendliness to the palate (7%), storageability of opened bottles (40%), and price (40%). Suppose that Bone
Ranch Wave has scores in these categories : clarity 4; bouquet 5; friendliness to the palate 3; storageabiliity 8;
and price 9. Use a weighted average to find its total rating. (5 pts.)