Transcript Slide 1

Here are the measurements of engine crankshafts. :
224.120 224.001 224.017 223.982 223.989 223.961
223.960 224.089 223.987 223.976 223.902 223.980
224.098 224.057 223.913 223.999
The data has a σ=.060
a) Construct and interpret a 95% confidence interval for the
process mean at the time these crankshafts were produced.
b) How large a sample would be needed to estimate the mean
within ±.020 mm with 95% confidence?
(10.65)
In a randomized comparative experiment on the effect of
calcium in the diet on blood pressure, researchers divided 54
healthy males at random into 2 groups. 1 group received
calcium, the other a placebo. A the beginning of the study, the
researchers measured many variables on the subjects. The
paper reporting the study gives xbar = 114.9 and s= 9.3 for the
seated systolic blood pressure of the 2 members of the
placebo group.
a) Calculate and interpret a 99% confidence interval (a t*
distribution) for the mean blood pressure in the population
from which the subjects were recruited. (10.67)
A nationwide random survey of 1500 adults asked about
attitudes toward “alternative medicine” such as acupuncture,
massage therapy, and herbal therapy. Among the
respondents, 660 said they would use alternative medicine if
traditional medicine was not producing the results they
wanted.
a) Construct and interpret a 95% confidence interval for the
proportion of all adults who would use alternative medicine.
(10.69)
A Gallup Poll asked a sample of Canadian adults if they thought the law
should allow doctors to end the life of the patient who is in great pain
and near death if the patient makes a request in writing. The poll
included 270 people in Quebec, 221 of whom agree that doctor assisted
suicide should be allowed.
a) What is the margin of error for a 99%confidence interval for the
proportion of alll Quebec adults who would allow doctor assisted
suicide.
b) How large a sample is needed to get the common ± 3 percentage
points margin of error.
(10.70)
How much do users pay for Internet service? Here are the monthly fees
paid by a random sample of 50 users of commercial internet in August
2000:
20 40 22
22
21
21
20
10
20
20
20 13 18
50
20
18
15
8
22
25
22 10
20
22
22
21
15
23
30
12
9 20
40
22
29
19
15
20
20
20
20 15
19
21
14
22
21
35
20
22
a) Using a t-distribution calculate and interpret a 90% confidence interval for
the mean monthly cost of internet access in August 2000.
(10.71)
To assess the accuracy of a laboratory scale, a standard weight know to
weigh 10 grams is weighed repeatedly. The scale readings are
Normally distributed with unknown mean . The standard deviation of
the scale readings is known to be .0002 gram.
a) The weight is weighed five times. The mean result is 10.0023 grams.
Construct and interpret a 98% confidence interval for the mean of
repeated measurements of the weight.
b) How many measurements must be averaged to get a margin of error
of ±.0001 with 98% confidence. Show work.
(10.14)
Variation is inherent in the production of high resolution video terminals.
Careful study has shown that when the process is operating properly, the
standard deviation of the tension readings is σ = 43. Here are the tension
readings from an SRS of 20 screens from a single day’s production:
269.5
297
269.6
283.3
304.8
280.4
233.5
257.4
317.5
327.4
264.7
307.7
310
343.3
328.1
342.6
338.8
340.1
374.6
336.1
a) Using the 4 steps necessary for a confidence intervals construct and
interpret a 90% confidence inteval for the mean tension of all the screens
produced on this day.