PROBLEM SET 1
SOLUTIONS
ERCAN KARADAS
(To be handed in at the beginning of the class, July 9)
(1) Suppose that you have data on Education and annual Family Income of 10
individuals:
(a) Show the data in a scatter-plot chart.
(b) Calculate variance for bot
PROBLEM SET 3
SOLUTIONS
ERCAN KARADAS
(To be left to the box in front of my oce at or before 5pm, Friday-July 20. My
oce is at 19 West 4th, 7th oor, room 717.
Randomly chosen two problem will be graded)
(1) Let us dene a random variable X as the number of
PROBLEM SET 1
ERCAN KARADAS
(To be handed in at the beginning of the class, July 9)
(1) Suppose that you have data on Education and annual Family Income of 10
individuals:
(a) Show the data in a scatter-plot chart.
(b) Calculate variance for both Educatio
PROBLEM SET 2
SOLUTIONS
ERCAN KARADAS
(To be handed in at the beginning of the class, July 16.
Randomly chosen two problem will be graded)
(1) Sample space for a dart game with 10 possible scores.
In this type of questions it is useful rst try to give an
PROBLEM SET 3
ERCAN KARADAS
(To be left to the box in front of my oce at or before 5pm, Friday-July 20. My
oce is at 19 West 4th, 7th oor, room 717.
Randomly chosen two problem will be graded)
(1) A contractor estimates the probabilities for the number of
PROBLEM SET 3
ERCAN KARADAS
(To be handed in at the beginning of the class, July 23.
Randomly chosen two problem will be graded)
(1) A contractor estimates the probabilities for the number of days required to
complete a certain type of construction projec
Chapter 4:
Discrete Random Variables and Probability Distributions
4.1 Daily computer sales is a discrete random variable that can take on no more than a countable number of values 4.2 The number of defective parts produced in daily production is a discre
PROBLEM SET 2
ERCAN KARADAS
(To be handed in at the beginning of the class, July 16.
Randomly chosen two problem will be graded)
(1) Consider the following experiment: Suppose that I brought a dart board to
the class, and I started to play with one you th
PROBLEM SET 4
ERCAN KARADAS
To be handed in at the beginning of the class, July 30.
(Randomly chosen two problem will be graded)
(1) It is estimated that the time that a well-known rock band, the Living
Ingrates, spends on stage at its concerts follow a n
PROBLEM SET 2
ERCAN KARADAS
(To b e handed in at the beginning of the class, July 16.
Randomly chosen two problem will be graded)
(1) Consider the following exp eriment: Suppose that I brought a dart board to the class,
and I started to play with one you
SOLVED PROBLEMS
ERCAN KARADAS
(1) Three distinct integers are chosen at random from the rst 20 positive
integers. Compute the probability that
(a) their sum is even
(b) their product is even
Solution
(a) Sum of three integers is even if and only if all of
ALGEBRA OF SETS
ERCAN KARADAS
Remember we discussed in the rst lecture that one of the main goal in statistics is to draw conclusions about a populations of objects by looking at some
appropriately chosen sample. The process of obtaining information from
PROBLEM SET 5
ERCAN KARADAS
To be handed in at the beginning of the class, August 6.
(Randomly chosen two problem will be graded)
(1) (7.3) A random sample of 10 economists produced the following forecasts
for percentage growth in real domestic product in
BASIC PROBABILITY
ERCAN KARADAS
Contents
1. Probability Postulates
In the previous section we have seen how to dene the sample space for an
experiment, and we have talked about what we mean by an event dened on a
sample space . In this section, we will be
Chapter 16:
Time-Series Analysis and Forecasting
16.1 Interpret the Laspeyres Price Index numbers provided with year 2000 as the base period. Interpret the results when the index for year 2003 is: a. 134.5. The total cost of purchasing the quantities trad
Chapter 15:
Analysis of Variance
15.1
Given the Analysis of Variance table, compute mean squares for between and for within groups. Compute the F ratio and test the hypothesis that the group means are equal. H 0 : 1 = 2 = 3 = 4 = 5 , H1 : otherwise SSG SS
Chapter 14:
Analysis of Categorical Data
14.1 H 0 : first preferences are evenly distributed across the three books. H1 : otherwise
Book Observed Number Probability (Ho) Expected Number Chi-square calculation Made Easy 17 0.333 20 0.45 Without Tears Profi
Chapter 13:
Additional Topics in Regression Analysis
13.1
Yi = 0 + 1 X 1i + 2 X 2i + 3 X 3i + 4 X 4i + i where Yi = College GPA X1 = SAT score X2 = 1 for sophomore, 0 otherwise X3 = 1 for junior, 0 otherwise X4 = 1 for senior, 0 otherwise The excluded cat
Chapter 11:
Simple Regression
11.1
a. Prepare a scatter plot.
Cov ( x, y ) 3.25 = = 0.65 2 5 sx c. Compute b0 = y b1 x = 7 0.65(4) = 4.4 b. Compute b1 = xi
1 3 4 5 7 20
y i ( xi x ) ( xi x ) 2 ( y i y ) ( y i y ) 2 ( xi x ) ( y i y )
5 7 6 8 9 35 -3 -1 0
Chapter 10:
Hypothesis Testing: Additional Topics
10.1 n = 25 paired observations with sample means of 50 and 60 for populations 1 and 2. Can you reject the null hypothesis at an alpha of .05 if a. sd = 20, H 0 : 1 2 = 0; H 1 : 1 2 > 0; 10 0 t= = 2.500, p
Chapter 9:
Hypothesis Testing: Single Population
9.1 9.2
H : p .2; H : p < .2;
0 1
H H
: No change in interest rates is warranted : Reduce interest rates to stimulate the economy 1
0 0 A
9.3
H :p
p p
B
: There is no difference in the percentage of underfi
Chapter 8:
Estimation: Additional Topics
8.1
a. Find the 95% confidence interval for the difference in means s 2.8 d tn 1, 2 d = 25.4 2.145 = 23.8493 up to 26.9507 nd 15 b. Find the margin of error for a 95% confidence interval s 2.8 ME = tn 1, 2 d = ME =
Chapter 7:
Estimation: Single Population
7.1
a. Check for nonnormality
The distribution shows no significant evidence of nonnormality. b. Point estimate of the population mean that is unbiased, efficient and consistent. X 560 Unbiased point estimator is t
Chapter 6:
Sampling and Sampling Distributions
6.1
a. Probability distribution for one die: Die outcome 1 2 3 4 5 6
Probability 1/6 1/6 1/6 1/6 1/6 1/6
b. Sampling distribution of the sample means from rolling a pair of dice: x Total Sample Prob. of x 2 1
Chapter 3:
Probability
3.1 3.2
A is the complement of event A and contains all of the samples points that are not in event A. Therefore, A = (E2, E4, E5, E7, E8, E10) a. A intersection B contains the sample points that are in both A and B. The intersectio
Chapter 2:
Describing Data: Numerical
2.1 Cruise agency number of weekly specials to the Caribbean: 20, 73, 75, 80, 82 a. Compute the mean, median and mode x 330 x = i = = 66 n 5 median = middlemost observation = 75 mode = no unique mode exists b. The med
Chapter 1:
Describing Data: Graphical
1.1 a. Numerical discrete. The number comes from a counting process. b. Numerical discrete. Since the response is an actual cost, it is discrete because the value comes from a counting process. c. Numerical discrete.