bus 172 practice maths
TRANSCRIPT
Problem set #1
8. Coast Star Sales Corporation is a West Coast wholesaler that markets to several
manufacturers of leisure products. Coastal Star has an 80-person sales force that sells
to wholesalers in a six-state area divided into two sales regions. The table below gives
the names from a sample of 11 salespersons, some descriptive information about each
sales person, and the sales performance of each for the past two years.
Region Salesperson Age Years of
Experience
Previous
Year Sales
Current
Year Sales
Difference
Northern Jackson 40 7 $412,744 $411,007 ($1,737)
Northern Gentry 60 12 $1,492,024 $1,726,630 $234,606
Northern La Forge 26 2 $301,421 $700,112 $398,691
Northern Miller 39 1 $401,241 $471,001 $69,760
Northern Mowen 64 5 $448,160 $449,261 $1,101
Southern Young 51 2 $518,897 $519,842 $945
Southern Fisk 34 1 $846,222 $713,333 ($132,889)
Southern Kincaid 62 10 $1,527,124 $2,009,041 $481,917
Southern Krieger 42 3 $921,174 $1,030,000 $108,826
Southern Manzer 64 5 $463,399 $422,798 ($40,601)
Southern Weiner 27 2 $548,011 $422,001 ($126,010)
Mean
age in
years
Mean
years of
experience
Total Total Difference
46.27 4.55 $7,880,417 $8,875,026 $994,609
Calculate a mean and a standard deviation for each variable and set a 95 percent confidence
interval around the mean for each variable.
Solution:
By Microsoft Excel Add-Ins
Megastat Descriptive statistics
Descriptive statistics
Age
Years of
Experience
Previous Year
Sales Current Year Sales
count 11 11 11 11
mean 46.27 4.55 716,401.55 806,820.55
sample variance 213.02 13.87 188,471,636,227.47 313,652,719,971.07
sample standard deviation 14.60 3.72 434,133.20 560,047.07
confidence interval 95.%
lower 36.47 2.04 424,746.89 430,575.81
confidence interval 95.%
upper 56.08 7.05 1,008,056.20 1,183,065.28
9. Calculate a median, mode, and range for each variable in question 8.
Solution:
By Microsoft Excel Add-Ins
Megastat Descriptive statistics
Descriptive statistics
Age
Years of
Experience
Previous Year
Sales
Current Year
Sales
count 11 11 11 11
minimum 26 1 301421 411007
maximum 64 12 1527124 2009041
range 38 11 1225703 1598034
1st quartile 36.50 2.00 430,452.00 436,029.50
median 42.00 3.00 518,897.00 519,842.00
3rd quartile 61.00 6.00 883,698.00 871,666.50
interquartile
range 24.50 4.00 453,246.00 435,637.00
mode 64.00 2.00 #N/A #N/A
10. Organize the data on current year sales in question 8 into a frequency distribution with the
following classes, (a) under $500,000, (b) $500,001 to $999,999, and (c) $1,000,000 and over.
Solution:
The frequency distribution for the current year sales
Class interval Frequency
under $500,000 5
$5000,001 to $999,999 3
$1000,000 and over 3
11. Organize the data on years of selling experience in question 8 into a frequency distribution
consisting of two classes: less than 5 years or 5 or more years.
Solution:
The frequency distribution for the years of selling experience
Class interval Frequency
less than 5 years 6
5 or more years 5
17. In a salary of 500, 60 percent responded positively to an attitude question. Calculate a
confidence interval at 95 percent to get an interval estimate for a proportion.
Solution:
By Microsoft Excel Add-Ins
Megastat Confidence intervals/ Sample size
Confidence interval - proportion
95% confidence level
0.12 proportion
500 n
1.960 z
0.028 half-width
0.148 upper confidence limit
0.092 lower confidence limit
18. In a nationwide survey, a researcher expects that 30 percent of the population will agree with
an attitude statement. She wishes to have less than 2 percent error and to be 95 percent
confident. What sample size is needed?
Solution:
By Microsoft Excel Add-Ins
Megastat Confidence intervals/ Sample size
Sample size - proportion
0.02 E, error tolerance
0.3 estimated population proportion
95% confidence level
1.960 z
2016.766 sample size
2017 rounded up
19. City Opera, a local opera company, wishes to take a sample of its subscribers to learn the
average number of years people have been subscribing. The director of research expects the
average to be 12 years and believes the standard deviation will be about 2 years (approximately
one-sixth of the range). She wishes to be 95 percent confident of her estimate. What is the
appropriate sample size?
Solution:
By Microsoft Excel Add-Ins
Megastat Confidence intervals/ Sample size
Sample size - mean
0.1667 E, error tolerance
2 standard deviation
95% confidence level
1.960 z
552.949 sample size
553 rounded up
20. A researcher expects the population proportion of Cubs fans in Chicago to be 80 percent.
The researcher wishes to have an error of less than 5 percent and to be 95 percent confident of an
estimate to be made from a mall survey. What sample size is required?
Solution:
By Microsoft Excel Add-Ins
Megastat Confidence intervals/ Sample size
Sample size - proportion
0.05 E, error tolerance
0.8 estimated population proportion
95% confidence level
1.960 z
245.853 sample size
246 rounded up
21. An automobile dealership plans to conduct a survey to determine what proportion of new car
buyers continue to have their cars serviced at the dealership after the warranty period ends. It
estimates that 30 percent of consumers do so. It wants the results of the survey to be accurate
within 5 percent, and it wants to be 95 percent confident of the results. What sample size is
necessary?
Solution:
By Microsoft Excel Add-Ins
Megastat Confidence intervals/ Sample size
Sample size - proportion
0.05 E, error tolerance
0.3 estimated population proportion
95% confidence level
1.960 z
322.683 sample size
323 rounded up
Problem set #2
2. In what types of situations is conducting a census more appropriate than sampling? When is
sampling more appropriate than taking a census?
Solution:
Situations where census more appropriate than sampling
Census is a survey conducted to the whole population without missing a single unit. Census
survey is conducted in situations like finding the socio economic status of the people in a
particular place here census is used rather than sampling survey because sampling will select
only some units in random and analyses but census is the appropriate survey to find the status of
the people in the whole population without missing a single unit.
Situations where sampling more appropriate than taking a census
Sampling is a technique which is used to consider a portion of the population. Sampling survey
is used in situations like for example the frequency of coffee consumption per day of people can
be studied by sampling technique rather census because most of the people have similar habits
and they won’t differ.
4. Describe the difference between a probability sample and a non-probability sample.
Solution:
In probability sampling the samples are selected at random but it is not in the case of non
probability sample. In probability sampling every population have to be considered with some
specified sampling schemes to be followed but it is not in non probability sample selection.
5. Comment on the following sampling designs:
A citizens group interested in generating public and financial support for a new university
basketball arena has published a questionnaire in area newspapers. Readers return the
questionnaires by mail.
Solution:
Mailed survey is used to collect samples through mail from the respondents.
A department store that wishes to examine whether it is losing or ganining customers dras
a sample from its list of credit card holders by selecting every tenth name.
Solution:
Systematic sampling design is used because it is mentioned as every tenth name is selected so
this sampling scheme that best used is Systematic sampling
A motorcycle manufacturer decided to research consumer characteristics by sending 100
questionnaires to each of its dealers. The dealers would then use their sales records to trace
buyers of this brand of motorcycle and distribute the questionnaires to them.
Solution:
Expert Sampling procedure is used because the data was collected by the dealers who have all
the details about their buyers.
A research company obtains a sample for a focus group through organized groups such as
church groups, clubs, or schools. The organizations are paid for securing respondents, and no
individual is directly compensated.
Solution:
Expert Sampling procedure is used because the data was collected by the organization who have
assigned the groups where the sample have to collected.
A banner ad on a business-oriented Website reads, “Are you a large company Sr.
Executive. Qualified execs receive $50 for under 10 minutes of time. Take the survey now!” Is
this an appropriate way to select business executives?
Solution:
Convenience sampling procedure is followed to select the business executives.
8. What are the benefits of stratified sampling?
Solution:
In stratified sampling the samples are selected at random using probability sampling scheme.
This sampling scheme is the more efficient scheme compared to other sampling designs because
in this sampling technique exact estimates of the population will be obtained for the variable of
interest. Efficient results were obtained because of the population being enforced to have equal
strata.
10. Outline the step by step procedure you would utilize to select the following:
A sample of 150 students at your college or university
Solution:
Systematic sampling procedure can be used to collect samples in random. We know the
population size that is the total strength of the college or the university that is N, the sample size,
n that is given as 150. The random sample is selected as k= N/n. every kth unit is selected upto
150 units in the sample
A sample of 50 light users and 50 heavy users of beer in a shopping mall intercept sample
Solution:
By going to any of the liquor shop and just by interviewing the customer who buys beer and
collect samples.
A sample of 50 mechanical engineers, 40 electrical engineers, and 40 civil engineers
from the subscriber list of an engineering journal
Solution:
First the subscriber list of engineering journal have to separated as mechanical engineers,
electrical engineers and civil engineers. Then keeping each of the three groups separate as the
population and by systematic sampling the random sample is selected as k= N/n. every kth unit is
selected upto each of the sample units of engineers specified. Where N is the population size and
n is the sample size.
A sample of banks, savings and loans, and other financiers of home mortgage loans
Solution:
The sample was collected from the people randomly and found their savings like which type of
saving modes they are using like most of the people will have bank account and savings in bank
like those saving details where obtained personally by interviewing the individuals.
A sample of male and female workers to compare hourly wages of drill press operators
Solution:
This sample is collected from the management of the organization about the hours worked by
their employees and then separating them as male and female.
11. Selection for jury duty is supposed to be a totally random process. Comment on the
following computer selection procedures and determine if they are indeed random.
A computer program scans the list of names and picks names that are next to those from
last scan.
Solution:
It is not certainly random in selecting the names because the list of names will be in the same
order so if we need as in random order means one and again you have to shuffle the list and enter
the names.
Three-digit numbers are randomly generated to select jurors from a list of licensed
drivers. If the weight information listed on the license matches the random number, the person is
selected.
Solution:
Generating of random number using software is with the help of the random number the person
is selected by matching the number with weight information this is certainly random selection.
The juror source list is obtained by merging a list of registered voters with a list of
licensed drivers.
Solution:
The merging is not of the same characteristic and it was not the right procedure.
1. How do multivariate statistical methods differ from univariate and bivariate methods?
Solution:
Multivariate statistical methods differ from univariate and bivariate methods because univariate
statistical method covers only descriptive statistics and some small sample and large sample
hypothesis test like t- test, z test, analysis of variance, non parametric are covered which are
basic and univariate methods are those which uses single dependent variable. In bivariate the
analysis will be done for two variables whereas multivariate methods use a linear combination of
dependent variables.
2. What is the distinction between dependence methods and independence methods?
Solution:
The difference between a dependence method and independence methods is in dependence
method the hypothesis to be analysis about that variable itself but in independence method two
groups of independent variables will be there comparison of those variables the analysis will be
conducted.
3. What is the aim of multiple linear regression? Discriminant analysis? Canonical
correlation? Multivariate analysis of variance?
Solution:
The aim of multiple linear regression to predict the dependent variable for several independent
variables. The main objective of regression analysis to find the linear relationship of the
dependent which is explained on the independent variables.
Discriminant analysis is a multivariate technique used in particular purposes when there are more
than two integral groups which are the independent measures. In discriminant analysis also the
prediction is made and the groups were tested whether they differ on the basis of the measures.
Canonical correlation is a analysis done two sets of variable and each set has two or more
variables in that set itself. The aim of this analysis is to find the relationship between the two sets
of variables.
Multivariate analysis of variance is a linear combination of the dependent variable which best
differentiates among the sets in the particular experimental design.
4. Give an example of a situation in which each of the techniques mentioned in question 3
might be used.
Solution:
An example multiple regression analysis is to predict the sales of a product which depends on the
working hours, cost and rating of the quality.
An example for a discriminant analysis is that predicting the patients who recovered from coma
stage. The independent variables considered are the details of the coma patient that is age, sex,
health condition, the time between the arrival date and got in coma stage. Here discriminant
analysis predicts the recovery of the coma patients with the different independent variables.
An example of a canonical correlation is considering the relationship between the two groups of
variables one is psychological variables are locus of control, self concept and motivation. The
other group is the academic variables that are reading, writing, math and science.
An example of multivariate analysis of variance has the four dependent variables with two
factors called sex and age which are nominal contrasts.
5. What is the aim of factor analysis? Cluster analysis? Multidimensional scaling?
Solution:
Factor analysis is a used to depict the variability among the observed variables in provisions of
some unobserved variables called factors. The observed variables are modeled as linear
combinations of the factors plus error terms.
Cluster analysis is a data analysis tool for solving groups of cases, so that the degree of
association is strong between members of the same cluster.
Multidimensional scaling is an alternative of factor analysis because it describes about observed
similarities of differences between the inspected items.
6. Give an example of a situation in which each of the techniques mentioned in question 5
might be used.
Solution:
An example for factor analysis is the physiologist takes two variables as IQ level that is verbal
intelligence and mathematical intelligence both the variable cannot be evaluated just by
observing. It cannot be valued by the scores for the 20 different academic fields of 2000 students.
The students are selected at random. The scores of the two groups of all the students who share
some same pairs of values for both verbal and mathematical intelligence is some constant times
their level of verbal intelligence plus another constant times their level of mathematical
intelligence
An example of cluster analysis is that the type of business unit with dissatisfied products
mentioned by respondent and dissatisfied services mentioned by respondent. cluster analysis
works by arranging the respondent into various groups to obtain the similarities and differences
in order to find the number of clusters that explain the data.
7. Why have computer software programs increased in the use of multivariate analysis?
Solution:
Software programs have increased in the use of multivariate analysis because it is easy to
compute the multivariate problems instead of working out manually takes a lot of time and some
human error in large calculation and it is time consuming to make it manually. But the software
just in a moment calculates and gives exact answers.
8. Why might a researcher want to use multivariate analysis rather than a univariate or
bivariate analysis technique?
Solution:
Multivariate analysis will study in detail about the variables where the univariate analysis cannot
because of single variable and the bivariate analysis too cannot because they are of limited use of
the dependent variables but multivariate is a linear combination of variables.