Homework 1
due date
1. Suppose the population mean account balance for a particular mutual
fund is μ = $5,500 and the population standard deviation,  = $660.
Assume the distribution of account balances is approximately normal.
Find the following probabilities.
a. P(5400< X <5600) for sample size, n=121
b. P(5400< X <5600) for sample size, n=196
c. Why is the answer to part b larger than that for part a?
d. P(5400<X<5600)
e. Why is the answer for part d smaller than that for part b (or a)?
f. What is the chance a randomly selected account will have a balance
within $660 of the population mean?
g. What is the chance a randomly selected account will have a balance
within $1320 of the population mean?
h. Explain why we have to know the exact distribution of the account
balances to answer questions d, f and g but not for questions a and b.
2. Suppose the College of Business and Economics at CSULA claims that
the average size of its lower division classes is thirty students. You
suspect that the actual average class is larger. You test this claim by
randomly sampling 45 different sections of lower division classes this
quarter. A sample mean of 32 students is calculated with a standard
deviation of 5.5. Perform a one tailed hypothesis test placing the business
school’s hypothesis within H0. Use a 5% level of significance.
3. It is generally understood that 35% of the undergraduate students in the
business school at CSULA currently receive financial aid. You suspect
the proportion receiving aid is smaller. You survey 250 students and find
75 currently receive financial aid.
a. Does the population you are sampling consist of all students at
CSULA?
b. Perform a one-tailed hypothesis test placing your hypothesis within
H1. Use a level of significance of .01.
4. Suppose the CEO of a major corporation wants to get an idea of the
income of the company's average stockholder. He surveys a sample of
400 individual shareholders attending the annual July stockholders
meeting. The CEO obtains a sample mean yearly income of $113,000
and a sample standard deviation of $18,000.
a. Define the population.
b. Calculate a 95% confidence interval for the population mean.
c. Explain what information the confidence interval gives the CEO that
he did not previously obtain with X .
d. Define what the population mean, μ, represents in the problem.
e. Given the definition of μ, give some reasons why the sampling
procedure (the little you know of it) could possibly be biased. What
does biasedness imply about the relationship between the sample
statistic X and the population parameter, μ?
f. Suppose the CEO came across a recent study of the company's
shareholders which implied the average stockholder had a yearly
income of $110,000. Carry out the following hypothesis using a 5%
level of significance:
H0: μ = 110,000
H1: μ ≠ 110,000
g. Explain how the results of your hypothesis test relate to the
confidence interval you constructed above.
5. The head of a chain of grocery stores hypothesizes that a typical store
serves, on an average weekday, 2,500 customers. To test the hypothesis,
the manager samples 40 of the grocery stores on a given weekday and
finds a sample mean of 2650 customers with a sample standard deviation
of 1000.
a. Test the following hypothesis at the 10% level of significance:
H0: μ = 2500
H1: μ ≠ 2500
b. Calculate the prob-value of the above test statistic.
6. It is generally understood that 20% of the undergraduate students in the
business school at CSULA have a GPA of at least a 3.0. You want to test
this hypothesis using sample data. You survey 150 students and find that
35 have a GPA of 3.0 or greater.
a. Perform a two-tailed hypothesis test using an alpha of .05.
b. Calculate the prob-value of the above test statistic.
Homework 2
due date
Below represents hypothetical data taken from a sample of Econ 309
students this quarter.
Student
Y – grade on econ
309 midterm exam
X1 – number of hours
studied for exam
X2 =1 if attended in-class
review session for exam
X2 =0 if not
I
83
6.5
0
II
92.5
6
1
III
67
4
1
IV
91
8
0
V
56
5
0
VI
77.5
6
1
A. Describe the apparent population based on the above sample data.
B. Regress the dependent variable Y only on X1 (ignore X2 for now).
C. Interpret the b1 coefficient you calculated. Explain why it makes sense
for the relationship to be positive.
D. Calculate and interpret the standard error of the regression.
E. Explain why we are not sure that the exact relationship found between
midterm grade and number of hours studied applies to the population of
309 students.
F. Calculate and interpret R2.
G. Calculate the sum of the residual terms. Why should the residual terms
sum to 0?
H. Estimate the standard error of b1.
I. Perform a two tailed hypothesis test in which the null hypothesis states
there is no relationship between midterm grade and number of hours
studied. Use a significance level of .10.
J. Calculate a 90% confidence interval for β1. What is the relationship
between the interval and the above hypothesis test?
K. Use Excel to regress Y on both X1 and X2.
L. Interpret the coefficient for number of hours studied. How does the
interpretation change?
M. Interpret the coefficient for the dummy variable. How is the
interpretation different from that for X1?
N. What is the predicted grade for a student who didn’t study at all but
attended the exam review session?