


Table 81 Mean Amounts to SpeedUp and Delay Consumption ($7 Record Store Gift Certificate) 

Time Interval 
Delay 
SpeedUp 
Significance 
1 week versus 4 weeks 
$1.09 
$.25 
.001 
4 weeks versus 8 weeks 
$.84 
$.37 
.005 
1 week versus 8 weeks 
$1.76 
$.52 
.001 
Source: Lowensteing (1988) 
Standard economics suggests that the value of an earlier coupon compared to a later one should not depend on which way the trade goes, from earlier to later or from later to earlier. Do these results support that assumption? Explain carefully.
18. Suppose that the diameters of oranges from a grove of orange trees is normally distributed. We wish to test the hypothesis that the mean diameter is three inches against the hypothesis that it is not equal to three inches. We are fairly certain that the true mean is three inches, so we do not want to abandon that assumption unless there is strong evidence against it, so we set the probability of Type I error at 5%. From the sample of 100 we find a standard deviation of one inch. When will reject the hypothesis that the true mean is three inches?
b) If the true mean is actually 3.2 inches, what is the probability that we will make Type II error by concluding that the true mean is three inches?
19. The output below comes from a statistical program:
One Sample Statistics: N Mean Std. Deviation Std Error Mean Variable 1
37
31.027
15.5768
2.5608
Test Value =30 t df sig (2tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper Variable 1
.401
36
.691
1.0270
4.1666
6.2206
20. The average SAT verbal score nationally in 1978 was 429 with a standard deviation of 110. Suppose we want to know whether students at our local college are different from this average.
21. A manufacturer of batteries wants to know whether its batteries are better or worse than the batteries of a competitor. The company's statistician knows that the company's batteries last an average of 1640 hours.
22. We have discussed how statistical inference resembles a trial by jury. Let's work though a couple problems to illustrate this, using some simple examples.
a) Suppose you have a die and you want to test it to see if it is a fair die, with equal chances of coming up with an even number (2, 4, 6) or an odd number (1, 3, 5). You toss the die 20 times. Using the table below, what is the probability that you will get exactly ten even tosses?
How many or how few even tosses would you have to get before you would conclude that the die was not fair? Explain. Put this in terms of a starting hypothesis and reasonable doubt.
20 trials, probability of success on any one trial = .5
Successes:
0
1
2
3
4
5
6
7
8
9
10Probability of n successes:
9.536743164e7
1.907348633e5
1.811981201e4
1.087188721e3
4.620552063e3
0.0147857666
0.0369644165
0.073928833
0.1201343536
0.1601791382
0.17619705211
12
13
14
15
16
17
18
19
200.1601791382
0.1201343536
0.073928833
0.0369644165
0.0147857666
4.620552063e3
1.087188721e3
1.811981201e4
1.907348633e5
9.536743164e7
b) A multiple choice test question has 20 questions on it, and each question has four possible answers.
If a person guessed at random, what is the probability that he or she would get exactly 6 right? (Use the table below.)
You are quite sure that John knows absolutely nothing and just guesses randomly on the test. How many questions would John have to get right before you would conclude he was not a complete knucklehead? Explain how you reach your decision.
20 trials, probability of success on any one trial = .25
Successes:
0
1
2
3
4
5
6
7
8
9
10Probability of n successes:
3.171211939e3
0.0211414129
0.0669478076
0.1338956152
0.1896854549
0.2023311519
0.1686092932
0.1124061955
0.0608866892
0.0270607508
0.009922275311
12
13
14
15
16
17
18
19
203.006750085e3
7.516875212e4
1.54192312e4
2.569871867e5
3.426495823e6
3.569266482e7
2.799424692e8
1.55523594e9
5.456968211e11
9.094947018e13
23. The output below comes from a statistical program:
One Sample Statistics: N Mean Std. Deviation Std Error Mean Age
115
66.2563
15.2338
1.4206
Test Value =70 t df sig (2tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper Age
2.635
144
.010
3.7437
6.5578
0.9295







Var2 
73 
230.1861 
5.1716 
_____ 














Var2 
_____ 
_____ 
.054 
1.1861 
.0205 
_____ 
24. "Patients treated with LUNESTA demonstrated statistically significant improvement (p<0.01) compared with placebo in patientreported measures of sleep latency (onset of sleep), wake time after sleep onset (WASO; a sleep maintenance measurement of the amount of time spent awake after initially falling asleep) and total sleep time for each week of the study. "
Explain what this quotation is saying to someone who has not had a course in statistics. In particular, what is the importance of the term "statistically significant" and what does the p<0.01 mean?
27. When a firm hires, it can make two mistakes. It can
hire someone who turns out to be a "bad" employee, or it can
pass over someone who would have been a "good" employee.
These mistakes are similar to the mistakes a jury can make
in a criminal trial and to Type I and Type II errors in
statistical hypothesis testing. We set up statistical
hypothesis testing so that we attack the claim. There are
two claims that we can use in hiring: the candidate is good
and we should hire unless there is reason to not hire, or
the candidate is bad and we should not hire unless there is
good reason to hire. Which should be the default position
if:
a) supply is large and training is expensive?
b) supply is small and training is inexpensive?
c) supply is small and training is expensive?
28. An official with the Federal Energy Administration believes that motorists are averaging more than 70 miles per hour on the interstate highways. As a result, he maintains that a more strict enforcement of speed limits would save a considerable amount of gasoline. To test his hunch, he plans to measure the speed of a large sample of motorists.
29. Below is an except from a book on pyramid power, the idea that pyramids have special powers. (For a larger image, click it.)

