1
Case Study
The Bureau of Labor Statistics collects data on employment and hourly
earnings in private industry groups and publishers its findings in
Employment
and Earnings
. Twenty people working in manufacturing industry are selected
at random: their hourly earnings, in dollars, are as follow:
16,70
7,44
13,78
16,49
7,49
17,92
17,21
5,51
10,40
10,75
15,27
19,72
10,68
13,10
14,70
15,55
16,67
15,07
14,02
15,99
Find 95% confidence interval for the mean hourly earnings, of all people
employed in the in manufacturing industry. Assume the population standard
deviation of the hourly earnings is $3,25.
What is the margin error?
Case Study
In 1908 William S. Gosset published the article “
The Probable Error of the
Mean
” (
Biometrika, Vol.6, pp.1-25
). It is in this pioneering paper, published
under the pseudonym “Student”, that he introduced what later became
known as
Student’s t
-distribution
. As an example, Gosset used following data
set, which gives the additional sleep in hours obtained by 10 patients using
laevohysocyamine hydrobromide
.
1,9
0,8
1,1
0,1
-0,1
4,4
5,5
1,6
4,6
3,4
Find 95% confidence interval for the additional sleep that would be obtained
on the average for all people using
laevohysocyamine hydrobromide
.
Does it appear that the drug is effective in increasing sleep?

2
Case Study
Forbes (January 3, 1994)
gave the following data about percentage return on
capital
(12
months)
for
representative
stocks
in
the
entertainment/information sector. Stocks such as CBS, Turner Broadcasting,
Walt Disney, Time Warner, Gannet, and so on were included.
29,7
21,1
6,5
10,0
9,0
3,6
2,4
23,5
9,3
9,7
10,6
5,5
12,3
1,7
22,0
21,7
28,9
26,9
14,9
13,7
9,6
2,3
7,1
12,9
10,3
10,9
8,1
8,1
10,8
8,2
7,0
11,0
10,0
5,5
3,0
4,8
6,5
19,1
17,2
4,6
14,5
Find 80% confidence interval for the average percentage return on capital for
all stocks in this sector.
If
someone
told
you
that
the
average
return
on
capital
in
the
entertainment/information sector was soon going to have a percentage
return above 24%, would you have reason to suspect that this might not
happen? Explain using the confidence interval.
In the investment business, sometimes the low end of a confidence interval is
called
a support
(
the quantity is not likely to go below this value
).
The high
end of a confidence interval is called
a resistance
(
the quantity is not likely to
rise above this value
).
Find
a support
and
a resistance
value for 90% credibility. Describe the margin
error. Check the relative error of this estimate.

3
Case Study
The Roman Arches
is an Italian restaurant.
The manager wants to estimate
the average amount a customer spends on lunch Monday through Friday.
A
random sample of 115 customers’ lunch tabs gave a mean of $9,74 with
standard deviation $2,93.

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- Spring '16
- Statistics, Standard Deviation, Mean