Statistics TEST 1
Due: October 2nd
at 9 pm No late papers will be
accepted. SHOW ALL WORK!
Directions for this assignment: Answer all questions. Please show all
work, writing explanations of intermediate steps wherever appropriate. Clearly label all graphs, including the scale
on the horizontal and vertical axes and the units of measure where appropriate.
You may
use your notes, your textbook, any other resource book, a graphing calculator
or computer software (subject to the statement above about showing intermediate
steps) as resources.
The data attached is for a sample companies in
retail apparel and department stores (Source: Yahoo Finance Industry data for
Apparel, Department and Discount stores as of 2/11/14)
1. Make an ungrouped frequency distribution for Price to Book. Use the frequency distribution to find the
mean, median, mode and standard deviation for Price to Book.
2. Organize the data for Net Profit Margin in a grouped frequency distribution using -35 to
-30.1 as the class limits of the first
class. Make a relative frequency
histogram. Describe the shape of the histogram.
Predict, from the shape of the histogram, whether the mean is greater
than the median or vice-versa. Calculate
the mean and the median. Was your
prediction correct?
3. Organize the data for Return on Equityin classes beginning with the class limits of -110
to -90.01. Draw an ogive for this data.
Use your ogive to estimate the median.
Then, find the actual median using the original data. Did the ogive provide a good estimate of the
median?
4. (a) Determine
the proportion of the Market Cap data
that lies within 1, 2, and 3 standard deviations of the mean. Determine, using the empirical rule, if the Market Cap data is approximately
normally distributed.
(b) Determine the proportion of the Price to Book data that lies within 1,
2, and 3 standard deviations of the mean.
Determine, using the empirical rule, if the Price to Book data is approximately normally distributed.
5. Find the z-score for Target for Market Cap. Also, find the z-score for Target for Return on Equity Describe, in a few sentences, the meaning of
these z-scores.
6.
Please access the article with URL: http://archinte.jamanetwork.com/article.aspx?articleid=1105943
Write answers in complete sentences to the following
questions:
a) What is the population?
b) What is the sample?
c) Is the data qualitative, discrete, or
continuous? EXPLAIN.
d) Describe the parameter. Give the value if possible.
e) Describe the statistic. Give the value if possible.
7. For each of the following, decide whether the mean, median, or mode
would be the most useful measure of central tendency. Explain each answer with at least one
complete sentence. (no explanation 
no points) Calculations are not necessary.
a) The following table gives the results of a
survey in which 2,400 consumers were asked to indicate which brand of soap they
purchased (most recent purchase).
|
Ivory |
20.2% |
|
Dove |
16.2% |
|
Softsoap |
7.7% |
|
Safeguard |
7.2% |
|
Irish Spring |
4.6% |
|
Others |
44.1% |
b) A marketing researcher wants to find the
income of the people who buy his company’s product. He finds the income of ten people who have
recently purchased the product. Five
earn twenty thousand, three earn thirty thousand, one earns forty thousand, and
one customer earns eighty thousand.
c) A recent study found that, in the US, the percent of electricity generated by coal
is 44.9%, by natural gas is 23.4%, 20.3%
by nuclear reactions, 6.9% by
hydroelectric, 3.6% by wind and solar power, and 1% is generated using
petroleum.
8. There are two brands of light bulbs. Ultralight bulbs that have lives with a mean
of 3000 hours with a standard deviation of 200 hours and Electrolyte bulbs
whose lives have a mean of 3000 hours with a standard deviation of 250
hours. Under what set of circumstances
would a purchasing manager want to purchase Ultralight? Explain thoroughly
why. Under what set of circumstances
would a purchasing manager want to purchase Electrolight? Explain thoroughly
why.
9. Two random samples were taken to determine
left foot length of female versus male bears based on measuring their tracks.
Numerical summaries of the data are given. Use them to answer the
questions.
A) Do male bears have longer feet than female
bears? Are you sure?
B) Give a range of values in which you would
expect to find 95% of all bears’ feet lengths.
Explain why you picked this range.
C) What is the shape of the distribution of
bears’ feet lengths? Explain.
EXTRA CREDIT : Consider the following data set with 10
observations:
2, 4, 5, 6, 8, 10, 12, 13, 14, X .
Find 3 different values of X for which
=
.
