Question 1
The data below consists of the number of shares traded on the NYSE for a sample of 18
companies on March 4, 2003.
Company Shares (000)
AllenTel 1393.4
BASF 98.4
CDI 11.9
CSX 983.5
Dover 657.6
Fluor 451.9
Grace 171.2
Hartmx 45.6
KCS 162.5
LizClaib 798.8
NuCor 763.4
Premcor 194.7
StJude 1595.5
Scripps 219.6
Sybase 304.6
Tootsie Roll 1299
Tyson 881.3
YorkIn 176.1
a) Set up a 95% confidence interval estimate of the population mean number of shares
traded for a company on the NYSE on March 4, 2003.
b) Based on previous studies, the standard deviation was estimated to be 500,000. Set up
a 95% confidence interval estimate of the population mean number of shares traded
for a company on the NYSE on March 4, 2003.
c) What sample size is needed if you want to be 95% confident of being correct to
within 200,000 shares?
d) Construct a 95% confidence interval of the population proportion of more than
500,000 shares traded for a company on the NYSE on March 4, 2003.
Question 2
Many companies have been experiencing downsizing. There is some feeling that when
rumors of a downsize begins to float through an organization, employees begin to use
their sick days at a faster rate than normal for fear of losing them. Fifty employees were
surveyed and asked if they would use their sick days freely in the face a potential
downsizing. Of the 50 employees, 20 said they would.
BFS1024 STATISTIC FOR FINANCE
2
a) Find a 95% confidence interval for the proportion of employees who would begin to
use their sick days freely when faced with a potential downsizing.
b) What sample size should be taken if the error in estimation is to be not more than 6%?
c) What sample size would be taken in the absence of any information on the proportion
of employees who would freely use their sick days when faced with a potential
downsizing?
Question 3
In a random sample of 20 students in MMU, the dean found that the mean time devoted
to homework per week was 14.3 hours with a standard deviation of 4 hours. Assume that
the homework time is normally distributed.
a) Estimate the 99% confidence interval of the weekly time spent doing homework for
all the MMU’s students.
b) How would your answer in part (a) change if the population standard deviation was
known to be 5 hours?
c) How many sample sizes have to be taken if the error in estimation should not be more
than 0.5 hour and if the population standard deviation was known to be 5 hours? Use
99% confidence interval (or ? = 0.01).
Question 4
A quality characteristic of interest for a tea-bag-filling process is the weight of the tea in
the individual bags. If the bags are underfilled, two problems arise. First, customers may
not be able to brew the tea to be as strong as they wish. Second, the company may be in
violation of the truth-in-labeling laws. Suppose that the label weight on the package
indicates that, on average, there are 5.5 grams of tea in a bag. On the other hand, if the
average amount of tea in a bag exceeds the label weight, the company is giving away
product. Below are weights in grams of a sample of 21 tea bags produced in the last hour
by a single machine.
5.65 5.52 5.33 5.44 5.54 5.29 5.36
5.59 5.35 5.51 5.50 5.30 5.48 5.57
5.42 5.57 5.50 5.47 5.48 5.60 5.44
a) Construct a 95% confidence interval of the population mean weight of the tea bags. Is
it reasonable to conclude that the population mean is 5.5 grams?
b) Construct a 90% confidence interval of the population proportion for weights less
than 5.5 grams as specified on the label of the package.
c) What sample size is needed if the company wants to be 99% confident of being
correct to within 10% of the population proportion for weights less than 5.5 grams as
specified on the label of the package?
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