12. Example #6
Ex18) A test of the breaking strengths of 6 ropes manufactured by a company showed a
mean breaking strength of 7750 lb and a standard deviation of 145 lb, whereas the
manufacturer claimed a mean breaking strength of 8000 lb. Can we support the
manufacturér’s claim at a level of significance of (a) 0.05, (b) 0.01? (c) W hat is the P value
of the test?
14. Example #7
Problem 1.
An astronomer wants to measure the distance from her observatory to a distant
star. However, due to atmospheric disturbances, any measurement will not yield
the exact distance d. As a result, the astronomer has decided to make a series of
measurements and then use their average value as an estimate of the actual
distance. If the astronomer believes that the values of the successive
measurements are independent random variables with a mean of d light years
and a standard deviation of 2 lig ht years, how many measurements need she
make to be at least 95 percent certain that her estimate is accurate to within ±.5
lig ht years?
16. Example #8
Problem 8.
O n O ctober 14, 2003, the N ew York Times reported that a recent poll indicated
that 52 percent of the population was in favor of the job performance of
President Bush, with a marg in of error of ± 4 percent. W hat does this mean? Can
we infer how many people were questioned?
17. Example #8
Problem 8.
O n O ctober 14, 2003, the N ew York Times reported that a recent poll indicated
that 52 percent of the population was in favor of the job performance of
President Bush, with a marg in of error of ± 4 percent. W hat does this mean? Can
we infer how many people were questioned?
18. Example #9
Problem 9.
Suppose that when a signal having value μ is transmitted from location A the
value received at location B is normally distributed with mean μ and variance σ2
but with σ2 being unknown. To reduce error, suppose the same value is sent 9
times. If 9 successive values are 5, 8.5, 12, 15, 7, 9, 7.5, 6.5, 10.5, compute a 95
percent confidence interval for μ.
19. Example #9 - Answer
Problem 9.
Suppose that when a signal having value μ is transmitted from location A the
value received at location B is normally distributed with mean μ and variance σ2
but with σ2 being unknown. To reduce error, suppose the same value is sent 9
times. If 9 successive values are 5, 8.5, 12, 15, 7, 9, 7.5, 6.5, 10.5, compute a 95
percent confidence interval for μ.
20. Example #10
Problem 2.
The time it takes a central processing unit to process a certain type of job is
normally distributed with mean 20 seconds and standard deviation 3 seconds. If
a sample of 15 such jobs is observed, what is the probability that the sample
variance will exceed 12?
21. Example #10 - Answer
Problem 2.
The time it takes a central processing unit to process a certain type of job is
normally distributed with mean 20 seconds and standard deviation 3 seconds. If
a sample of 15 such jobs is observed, what is the probability that the sample
variance will exceed 12?
23. Example #11 – Use of Computer
Problem 7.
A standardized procedure is expected to produce washers with very small
deviation in their thicknesses. Suppose that 10 such washers were chosen and
measured. If the thicknesses of these washers were, in inches,
what is a 90 percent confidence interval for the standard deviation of the
thickness of a washer produced by this procedure?
25. Example #12
Problem 12.
All cigarettes presently on the market have an average nicotine content of at least
1.6 mg per cig arette. A firm that produces cig arettes claims that it has discovered
a new way to result in the average nicotine content of a cigarette being less than
1.6 mg. To test this claim, a sample of 20 of the firm’s cig arettes were analyzed. If
it is known that the standard deviation of a cig arette’s nicotine content is .8 mg,
what conclusions can be drawn, at the 5 percent level of significance, if the
average nicotine content of the 20 cigarettes is 1.54?
N ote: The above raises the question of how we would know in advance that the
standard deviation is .8. O ne possibility is that the variation in a cigarette’s
nicotine content is due to variability in the amount of tobacco in each cigarette
and not on the method of curing that is used. Hence, the standard deviation can
be known from previous experience.
28. Example #13
Problem 13.
Among a clinic’s patients having blood cholesterol levels ranging in the medium
to high range (at least 220 milliliters per deciliter of serum), volunteers were
recruited to test a new drug desig ned to reduce blood cholesterol. A group of 50
volunteers was given the drug for 1 month and the changes in their blood
cholesterol levels were noted. If the average change was a reduction of 14.8 with
a sample standard deviation of 6.4, what conclusions can be drawn?
