Econ 2810
Intro to Statistics and Computing In Economics
Spring 2016
Problem Set 4
Out: April 7
Due: April 28
1. The data used in the table below came from a random sample.
Group 1
3.8
1.2
4.1
5.5
2.3
Group 2
5.4
2.0
4.8
3.8
Group 3
1.3
0.7
2.2
a. Complete the following ANOVA table. Please show your work.
Source
Group
df
SS
MS
F
Error
Total
b. Test the null hypothesis that µ1 = µ2 = µ3 , where µi represents the mean for group i. Use
α = 0.01.
2. Suppose the PGA wants to compare the mean distances associated with four different brands of golf
balls when struck with a driver. From a randomized sample, data is collected from a driver hitting a
random sample of 10 balls of each brand in a random sequences. The distance is recorded for each hit,
and the results are shown in the table below.
Brand A
251.2
245.1
248
251.1
260.5
250
253.9
244.6
254.6
248.8
Brand B
263.2
262.9
265
254.5
264.3
257
262.8
264.4
260.6
255.9
Brand C
269.7
263.2
277.5
267.4
270.5
265.5
270.7
272.9
275.6
266.5
Brand D
251.6
248.6
249.4
242
246.5
251.3
261.8
249
247.1
245.9
a. Set up the null and alternative hypotheses to compare the mean distances for the four brands
b. You can use statistical software (CrunchIt) to obtain the test statistic. Use α = 0.1. At this
significance level, can you reject the null hypothesis? Why?
[Please Turn Over]
1
2
3. The PGA is interested in knowing whether the difference in distance traveled by any two golf ball
brands depends on the club used. The PGA tests four different brands (A,B,C,D) of golf balls and two
different clubs (driver, five-iron) in a random experiment. The two-way table is presented below.
Club
Driver
Driver
Driver
Driver
Five-Iron
Five-Iron
Five-Iron
Five-Iron
Brand A
226.4
232.6
234
220.7
163.8
179.4
168.6
173.4
Brand B
238.3
231.7
227.7
237.2
184.4
180.6
179.5
186.2
Brand C
240.5
246.9
240.3
244.7
179
168
165.2
156.5
Brand D
219.8
228.7
232.9
237.6
157.8
161.8
162.1
160.3
a. Use statistical software (CrunchIt) to complete the following two way ANOVA table.
Source
Brand
df
SS
MS
F
P −value
Club
Brand*Club
Error
Total
b. Interpret the results of your analysis. Use α = 0.1 for each test you conduct.
4. Using CrunchIt, print out and attach the regression output using the Exercise 06 data set. The
dependent variable is the percent return on treasury bills (TBILL); the independent variable is the
rate of inflation.
a. Based on your regression output, is the coefficient on INFLATION statistically significant at the
1% level? Why?
b. Calculate the predicted value for TBILL when INFLATION=3.7.
