Statistics 13A – Spring 2010
Sample Midterm 1- Solutions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
Which of the following in not an element of inferential statistics?
A)
identification of patterns in the data
B)
the population of interest
C)
a measure of reliability for an inference made about the population
D)
using data obtained from a sample of the population
E)
one or more variable that are to be investigated
2)
A summary measure that is computed from a population to describe a characteristic is called
A)
a statistic.
B)
a variable.
C)
a census.
D)
a parameter.
E)
a data file
3)
A high school guidance counselor analyzed the data from a sample of 600 community colleges collected from throughout the United States. One of his goals was to estimate the annual tuition costs of community colleges in the United States. Identify the population of interest to the guidance counselor.
A)
all community colleges in the United States
B)
all high school guidance counselors
C)
community college tuition
D)
all students attending community colleges in the United States
E)
the sample of 600 community colleges
4)
When each of its observations belong to one of a set of categories, a variable is called
A)
qualitative.
B)
categorical.
C)
discrete.
D)
both a. and b.
E)
all of the above.
5)
Brandon kept track of the number of hours he spent exercising each week. The results for four months are shown below. Find the mean number of hours Brandon spent exercising per week. Round your answer to two decimal places.
A)
8.01
B)
7.79
C)
8.25
D)
7.38
E)
7.30
A nurse measured the blood pressure of each person who visited her clinic. Following is a relative-frequency histogram for the systolic blood pressure readings for those people aged between 25 and 40. Use the histogram to answer the question. The blood pressure readings were given to the nearest whole number.
6)
Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading less than 120?
A)
15%
B)
50%
C)
3.5%
D)
35%
E)
5%
7)
A relative frequency histogram for the heights of a sample of adult women is shown below. Identify the overall shape of the distribution.
A)
Bimodal
B)
Bell-shaped
C)
Multimodal
D)
Right skewed
E)
Left skewed
8)
The book cost (in dollars) for one semester's books are given below for a sample of five college students. Calculate the sample variance of the book costs.
340, 170, 145, 420, 120
A)
876.40
B)
160,482.50
C)
17,680.00
D)
136.250
E)
89,021.50
9)
Scores on a test have a mean of 73 and a standard deviation of 9. Michelle has a score of 91. Convert Michelle's score to a z-score. Round to the nearest hundredth.
A)
-2.00
B)
1.00
C)
18.00
D)
-18.00
E)
2.00
10)
Suppose you were to collect data for the pair of given variables in order to make a scatterplot. Determine for each variable if it is the explanatory variable or the response variable.
Variables: Minutes of homework, grade on exam
A)
Minutes of homework: explanatory variable
Grade on exam: response variable
B)
Minutes of homework: response variable
Grade on exam: explanatory variable
C)
Minutes of homework: response variable
Grade on exam: both
D)
Minutes of homework: both
Grade on exam: response variable
E)
Minutes of homework: explanatory variable
Grade on exam: both
11)
The partially filled contingency table gives the frequencies of the data on age (in years) and sex from the residents of a retirement home.
Age (yrs)
60-69 / 70-79 / Over 79 / TotalMale / 11 / 9 / 5
Female / 9 / 2 / 4
Total
Given that the resident is male, what is the proportion of residents in the age group 60-69?
A)
0.35
B)
0.44
C)
0.50
D)
0.60
E)
0.55
12)
Four pairs of data yield r = 0.942 and the regression equation . Also, . What is the best predicted value of y for x=2.9 ?
A)
12.75
B)
11.6
C)
0.942
D)
2.826
E)
8.7
13)
The prediction error for an observation, which is the difference between the actual value and the predicted value of the response variable, is called ______.
A)
a residual
B)
an extrapolation
C)
a correlation
D)
an intercept
E)
an outlier
14)
A)
= 12; = 1.00
B)
= 12; = 2.00
C)
= 48; =-18.00
D)
= 3; = 0.50
E)
= 3; = 1.00
15)
A stock analyst selects a stock from a group of twenty for investment by choosing the stock with the greatest earnings per share reported for the last quarter. What type of study is this?
A)
Experimental
B)
Observational
C)
Hypothetical
D)
Implied
E)
Unknown
16)
Given a group of students: Allen (A), Brenda (B), Chad (C), Dorothy (D), and Eric (E), list all of the possible samples (without replacement) of size four that can be obtained from the group.
A)
ABCD, ABCE, ACDE, ADEB, BCDE, BCEA, BDEA, CABD, CEDB, DACE
B)
ABCD, ABCE, ACDE, ADEB, BCDE
C)
ABCD, ABCE, ABDE
D)
ABCD, ABCE, ACDE, ADEB
E)
ABCD
17)
The name of each contestant is written on a separate card, the cards are placed in a bag, and three names are picked from the bag. What type of sampling is this?
A)
Convenience
B)
Matched pair
C)
Stratified
D)
Random
E)
Cluster
18)
The table below describes the smoking habits of a group of asthma sufferers.
What is the probability that a woman is a nonsmoker?
A)
0.345
B)
0.297
C)
0.479
D)
0.490
E)
0.703
19)
Two shipments of components were received by a factory and stored in two separate bins. Shipment (I) has 2% of its contents defective, while shipment (II) has 5% of its contents defective. If it is equally likely an employee will go to either bin and select a component randomly, what is the probability that a defective component came from shipment (II)?
A)
0.286
B)
0.2
C)
0.714
D)
0.384
E)
0.5
20)
60% of students at one college drink coffee, and 16% of people who drink coffee suffer from insomnia. What is the probability that a randomly selected student drinks coffee and suffers from insomnia?
A)
0.16
B)
0.96
C)
0.76
D)
0.096
E)
0.664
21) For a randomly selected student in a particular high school, let Y denote the number of living grandparents of the
student. What are the possible values of the random variable Y?
A) 4B) 0, 1, 2, 3, 4C) 1, 2, 3, 4D) 0, 1, 2E) 1, 2
22) When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below.
(1, 1)(1, 2)(1, 3)(1, 4)(1, 5)(1, 6)
(2, 1)(2, 2)(2, 3)(2, 4)(2, 5)(2, 6)
(3, 1)(3, 2)(3, 3)(3, 4)(3, 5)(3, 6)
(4, 1)(4, 2)(4, 3)(4, 4)(4, 5)(4, 6)
(5, 1)(5, 2)(5, 3)(5, 4)(5, 5)(5, 6)
(6, 1)(6, 2)(6, 3)(6, 4)(6, 5)(6, 6)
Let X denote the smaller of the two numbers. If both dice come up the same number, then X equals that common value. Find the probability distribution of X. Leave your probabilities in fraction form.
A): B): C): D): E):
23) Find the mean of the binomial random variable. On a 10-question multiple choice test, each question has four
possible answers, one of which is correct. For students who guess at all answers, find the mean for the random
variable X, the number of correct answers.
A) 2.5B) 3.3C) 1.9D) 7.5E) 5
24) Find the standard deviation of the binomial random variable. A die is rolled 18 times and the number of twos
that come up is tallied. If this experiment is repeated many times, find the standard deviation for the random
variable X, the number of twos.
A) 2.12B) 1.622C) 1.537D) 1.581E) 1.587
25) A basketball player has made 70% of his foul shots during the season. If he shoots 3 foul shots in tonight's game,
what is the probability that he makes all of the shots?
A) 0.09B) 0.686C) 0.027D) 0.21E) 0.343
26) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a
standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 170
and 220.
A) 0.6189B) 0.1554C) 0.0703D) 0.2257E) 0.3811
27) Which of the following is not true about the standard normal distribution?
A) About 68% of its observations fall between -1 and 1.
B) The total area under the standard normal curve is 1.
C) About 95% of its observations fall between -2 and 2.
D) The standard normal curve is symmetric about 0.
E) The area under the standard normal curve to the left of z = 0 is negative.
28) Find the z-score having area 0.86 to its right under the standard normal curve.
A) -1.08B) 0.8051C) 1.08D) -0.5557E) 0.5557
TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.
29)
A distribution that has the right tail longer than the left tail is called right skewed. TRUE
30)
Based on 12,000 responses from 55,000 questionaires sent to its alumni, a major university estimated that the annual salary of its alumini was $98,500 per year. Would this sampling provide a random sample? FALSE
31)
Descriptive statistics refers to methods of making decisions or predictions about a population, based on data obtained from a sample of that population; while, inferential statistics refers to methods for summarizing the data. FALSE
32)
In skewed distributions, we expect the values of the mean, median, and mode to be approximately equal, since they are all measures of center. FALSE
33)
If P(A) = 0.4, P(B) = 0.5, and P(A∩B) = 0.20, then the events A and B are independent. TRUE
34)
In studying the association between two variables, the data analysis examines how the outcome of the response variable depends on the value of the explanatory variable. FALSE
35)
The closer r is to 0, the weaker is the linear association between the variables. TRUE
36)
It is not possible to establish cause and effect definitively with observational studies. TRUE
37)
The plastic arrow on a spinner for a child's game stops rotating to point at a color that will determine what happens next. The following probability assignment is possible (assuming there are four colors red, yellow, green and blue). FALSE
Probability of ...
38) For independent events A and B, P(A|B) = P(A). TRUE
40) X ~ Binomial(4, 0.25), then P(X = 3) =0.0469. TRUE