Download Review for TEST I - Florida International University

Review for TEST 3
STA 3145
(Ch. 9, 11, 13)
Make sure to identify all elements of Test of Hypothesis and Confidence Interval, such as :
Point estimator, Sampling Error, Test statistic, Critical value, P-value, Rejection Region, Level of
significance, Error type I and II, Null and Alternate hypotheses. Good luck!
1. A salesman for a shoe company claimed that runners would record quicker times, on the average, with the
company's brand of sneaker. A track coach decided to test the claim. The coach selected eight runners. Each
runner ran two 100-yard dashes on different days. In one 100-yard dash, the runners wore the sneakers
supplied by the school; in the other, they wore the sneakers supplied by the salesman. Each runner was
randomly assigned the sneakers to wear for the first run. Their times, measured in seconds, were as follows:
Sneakers 1
Company 10.8
School
11.4
2
12.3
12.5
3
10.7
10.8
4
12.0
11.7
5
10.6
10.9
6
11.5
11.8
7
12.1
12.2
8
11.2
11.7
Note. For the differences, X D = -.225 and s D = .276. Assume the population of differences is approximately
normal.
2. A new insect spray, type A, is to be compared with a spray, type B, that is currently in use. Two rooms of
equal size are sprayed with the same amount of spray, one room with A, the other with B. Two hundred insects
are released into each room, and after 1 hour the numbers of dead insects are counted." There are 120 dead
insects in the room sprayed with A and 90 in the room sprayed with B. Do the data provide enough evidence to
indicate that spray A is more effective than spray B? Use α = .05.
3. To compare two methods of teaching reading, randomly selected groups of elementary school children
were assigned to each of the two methods for a 6-month period. The criterion for measuring achievement
was a reading comprehension test." The 11 students assigned to method I had a mean score of 64 with a
variance of 52. The 14 students assigned to method II had a mean score of 69 with a variance of 71. Do the
data provide enough evidence to indicate a difference in the mean scores on the comprehension test for the
two teaching methods? Use α = .01.
4. A study at the University of Michigan wants to determine student options regarding non-revenuegenerating athletics. Specifically, one question in a survey asks students "Do you think the women's
basketball program should be discontinued?" The data collected revealed that 100 of the 1,000 females
surveyed responded "Yes" and that 400 of the 1,000 males surveyed responded "Yes". Suppose a 99%
confidence interval resulted in the following confidence interval for the true difference in population
proportions: (-.5, -.1). Interpret the interval.
5. How does wives' employment status affect their husbands' well being? To answer this question, a survey
of the job satisfaction of 25 male accountants who were employed full-time and married was conducted. In
this sample, 15 wives were employed and 10 were unemployed. The goal of the study is to compare the
mean job satisfaction levels of the two groups of husbands: (1) those with working wives and (2) those with
unemployed wives. The observed significance level (p-value) of the test is .03. Is this sufficient evidence to
conclude that the mean satisfaction level of husbands with working wives is less than the mean satisfaction
level of husbands with unemployed wives? Test using  =.05.
I. Operations managers often use work sampling to estimate how much time workers
spend on each operation. Work sampling, which involves observing workers at
random points in time, was applied to the staff of the catalog sales department
of a clothing manufacturer. The department applied regression to the following
data collected for 40 consecutive working days:
TIME: y = Time spent (in hours) taking telephone orders during the day
ORDERS: x = Number of telephone orders received during the day
Initially, the simple linear model E(y) = β0 + β1x was fit to the data.
PREDICTOR
VARIABLES
--------CONSTANT
ORDERS
R2 = 0.7229
COEFFICIENT
----------10.1639
0.05836
STD ERROR
--------1.77844
0.00586
STUDENT'S T
----------5.72
9.96
P
-----0.0000
0.0000
S = 3.40844
1. Conduct a test of hypothesis to determine if time spent (in hours) taking telephone orders during the day and the
number of telephone orders received during the day are positively linearly related.
2. Give a practical interpretation of the correlation coefficient for the above output.
3. Give a practical interpretation of the coefficient of determination, R2.
4. Give a practical interpretation of the estimated slope of the least squares line.
5. Find a 90% confidence interval for β1. Give a practical interpretation.
6. Give a practical interpretation of the model standard deviation, s.
7. Give a practical interpretation of the estimate of the y-intercept of the least squares line.
8. Based on the value of the test statistic given in the problem, make the proper conclusion.
II. Example 13.2 on page 747
Suppose an educational TV station has broadcast a series of programs on the physiological
and psychological effects of smoking marijuana. Before the series was shown, it was
determined that 7% of the citizens favored legalization, 18% favored decriminalization,
65% favored the existing law, and 10% had no opinion. Test at the level to see whether these
data indicate that the distribution of opinions differs significantly from the proportions that
existed before the educational series was aired.
Ho:
Ha:
_______________
D.F. = _____
α = .05
RR: _________________
___________________
Test Statistic: _____________,
Decision: ___________________________________________
E(n1) = ________, E(n2) = ________, E(n3) = ________, E(n4) = ________.
prob
observed
0.07
0.18
0.65
0.10
39
99
336
26
chi-sq
expected
O - E
4
9
11
-24
= __________
O-E sq
16
81
121
576
terms
0.4571
0.9000
0.3723
11.5200
p-value = 0.00412732
III. The following table displays the educational level and social activity of employees from a certain company. A
researcher wants to determine whether association exists between an educational level and social activity of
employees. At the 0.01 level of significance conduct the appropriate test.
IV. A multinomial experiment with possible outcomes A, B, C, and D, and n = 400 observations produced the results
shown below.
H0 : PA = 0.3, PB = 0.25, PC = 0.25, PD = 0.2.
Class
Observed
A
126
B
104
C
96
D
74
V. The Example on page 754
The researchers investigated the relationship between the gender
of a viewer and the viewers brand awareness. 300 TV viewers were
asked to identify products advertised by male celebrity
spokespersons.
Ho: _________________________
α = .01
D.F. = _______
Ha: ____________________________
RR: ______________
χ2 = ____________________________ ,
E(n21) = ________,
E(n12) = ________.
Decision: ___________________________________________
male
female
Total
Yes
95
41
136
No
55
109
164
150
150
300
Total
ChiSq = 10.721 + 10.721 + 8.890 +
8.890 = 39.222
VI. Cocoon Problem
Researchers investigated the relationship between the mean daily air
temperature and the cocoon temperature of wooly-bear caterpillars of the
High arctic.
The regression equation is
Cocoon = 3.37 + 1.20 Air
Predictor
Constant
Air
s = 0.8558
Coef
Stdev
t
p
3.3747
1.20086
0.4708
0.09375
7.17
12.81
0.000
0.000
R-sq = 94.3%
Obs.
Air
1
2
3
4
5
6
7
8
9
10
11
12
1.7
2.0
2.2
2.6
3.0
3.5
3.7
4.1
4.4
4.5
9.2
10.4
Cocoon
3.600
5.300
6.800
6.800
7.000
7.100
8.700
8.000
9.500
9.600
14.600
15.100
Fit
St.Dev.Fit
5.416
5.776
6.017
6.497
6.977
7.578
7.818
8.298
8.658
8.779
14.423
15.864
Residual
0.345
0.326
0.314
0.293
0.274
0.258
0.253
0.248
0.247
0.248
0.524
0.625
-1.816
-0.476
0.98
0.38
0.03
-0.478
1.08
-0.298
1.03
1.00
0.26
-0.764
1) According to MINITAB, the least squares equation is _____________ .
2) When the air temperature was 4.4oC the cocoon temperature was
______, and the estimated cocoon temperature is ___________.
3) Since t = ____________ with p-value ____________, there _________
enough evidence at the 5% level to indicate that the to of the
related to the air temperature, for air to _________
cocoon is linearly
4) The estimated slope of the regression line is ___________.
5) The correlation coefficient for this data is r = ______. ; r2 = ____________.
6) Hence, we can conclude that ___________% of the variability in the
cocoon temperatures is explained by the estimated least squares line relating
cocoon temperature to air temperature.
7) Suppose we put a single woolly-bear caterpillar cocoon in a controlled
environment with the air temperature set at 7oC. Predict the cocoon
temperature.
VII. Real-estate investors, home buyers, and homeowners often use the appraised value of property as a basis
for predicting the sale of that property. Data on sale prices (y) and total appraised value (x) of 78 residential
properties sold in 2006 in an upscale Tampa, Florida, neighborhood are collected. The simple linear model:
E ( x)   0   1x , was fit to the data.
Regression Analysis: SALEPRICE versus APPVALUE
The regression equation is
SALEPRICE = 184 + 1.20 APPVALUE
Predictor
Constant
APPVALUE
S = 44859.7
Coef
184
1.19956
SE Coef
9834
0.02234
R-Sq = 97.4%
T
0.02
53.70
P
0.985
0.000
R-Sq(adj) = 97.4%
I. Give the correlation coefficient for the above output. Describe the nature of the relationship (if any) that exist
between the sale price for residential properties in this neighborhood and the appraised property value.
r
Interpretation:
II. Approximately what percentage of the sample variation in the sale price can be explained by the linear model?
________%
III. Complete the sentence:
“We expect approximately 95% of the observed sale prices to lie within _____________ points of their
__________________ values.
IV. Find and interpret the 95% confidence interval for  1 .
95% CI for  1
Interpretation:
V. Predict the estimated average sale price for residential properties in this neighborhood that have an appraised
property value of $400,000.