Download Homework - Miles Finney

Second Homework
1.
Ace Rental Cars is interested in estimating the mean number of miles its cars are driven on
the 4th of July holiday. From the 25,000 cars it owns, the company’s statistician selects
200 cars rented for the 4th and records the mileage for each car. The calculated sample
mean is 54.5 miles and the standard deviation is 65 miles.
a.
Define what the population mean is. What exactly is the sample mean estimating?
b.
Construct a 95% confidence interval for the population mean. Interpret.
c.
Construct a 90% confidence interval; interpret and compare to the interval
constructed for part b above.
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.
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.
4.
Suppose you survey 81 adult American males and record a mean weight of 194 pounds.
The sample standard deviation is 35 pounds.
a.
From the information given describe the population whose mean you are
estimating.
b.
Construct a 99% confidence interval for the population mean. Interpret.
c.
Suppose a prominent doctor contends that adult American males have a
population mean weight of 220 pounds. Using a level of significance of .01,
perform the hypothesis test:
H0: µ=220
H1: µ≠220
What is the relationship between the hypothesis test result and the constructed
confidence interval?
5.
An economist hypothesizes that the mean number of people living in rent controlled
apartments in New York City is two. You suspect the hypothesis is over-shooting the
actual population mean number of residents in such NY apartments. You collect data on
40 rent-controlled apartments and find a sample mean of 1.5 and sample standard
deviation of .75. Perform a one-tailed test using an alpha of .10.
6.
Below represents hypothetical data taken from a sample of Econ 309 students this
quarter.
Student
Y – grade on econ 309 X1 – number of hours
midterm exam
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?