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Examples:
EXAMPLE 1:
Incidence of tumours observed in control and treated mice in a preclinical study is as follows:


Controls - 1 of 14 animals
Treated - 6 of 14 animals
What is the aim of the study?
Our aim is to compare incidence of tumour between two unpaired groups (control vs treated).
EXAMPLE 2:
If a manufacturing company wants to compare the productivity of three or more employees based
on working hours.
EXAMPLE 3:
When a company wants to compare the employee productivity based on the working hours and
working conditions, if a company wants to compare employee productivity
EXAMPLE 4:
What is the effectiveness of a new programme between in reducing litter. Two cities were sampled,
the first measure was taken in July 2001, and the second measure in July 2002.
EXAMPLE 5:
A physician is interested in the effect of an anaesthetic on reaction times. Two groups are compared,
one with (A) and one without (B) taking the anaesthetic. Subjects had to react on a simple visual
stimulus, results were ranked on an ordinal scale. Reaction times are not normally distributed in this
experiment
EXAMPLE 6:
You want to find out how socioeconomic status affects attitude towards sales tax increases. Your
independent variable is “socioeconomic status” with three levels: working class, middle class and
wealthy. The dependent variable is measured on a 5-point Likert scale from strongly agree to
strongly disagree.
EXAMPLE 7:
Null Hypothesis: There is no correlation between Mathematics score and number of hours spent in
studying the Mathematics subject.
EXAMPLE 8:
Null Hypothesis: There is no difference between the Mathematics scores of Sections A and B.
EXAMPLE 9:
An e-commerce research company claims that 60% or more graduate students have bought
merchandise on-line. A consumer group is suspicious of the claim and thinks that the proportion is
lower than 60%. A random sample of 80 graduate students show that only 22 students have ever
done so. Is there enough evidence to show that the true proportion is lower than 60%? Conduct the
test at 10% Type I error rate, and use the p-value and rejection region approaches.
EXAMPLE 10:
The administrator at your local hospital states that on weekends the average wait time for
emergency room visits is 10 minutes. Based on discussions you have had with friends who have
complained on how long they waited to be seen in the ER over a weekend, you dispute the
administrator's claim. You decide to test you hypothesis. Over the course of a few weekends you
record the wait time for 40 randomly selected patients. The average wait time for these 40 patients
is 11 minutes with a standard deviation of 3 minutes. Do you have enough evidence to support your
hypothesis that the average ER wait time exceeds 10 minutes? You opt to conduct the test at a 5%
level of significance.
EXAMPLE 11:
Weight change in pounds of 14 female subjects after taking an exercise program for six weeks are
recorded:
17; 7; -4; -18; 2; 9; 12; 9; -12; -9; -18; -14; -18; -20
Is there sufficient evidence that the average weight change is different from 0? (set α = 0.05)
EXAMPLE 12:
You’re curious about whether people from Durban and those from Johannesburg spend a different
amount of money per month on movies.
EXAMPLE 13:
A medical researcher has heard anecdotal evidence that certain anti-depressive drugs can have the
positive side-effect of lowering neurological pain in those individuals with chronic, neurological back
pain, when administered in doses lower than those prescribed for depression. The medical
researcher would like to investigate this anecdotal evidence with a study. The researcher identifies 3
well-known, anti-depressive drugs which might have this positive side effect, and labels them Drug
A, Drug B and Drug C. The researcher then recruits a group of 60 individuals with a similar level of
back pain and randomly assigns them to one of three groups – Drug A, Drug B or Drug C treatment
groups – and prescribes the relevant drug for a 4 week period. At the end of the 4 week period, the
researcher asks the participants to rate their back pain on a scale of 1 to 10, with 10 indicating the
greatest level of pain. The researcher wants to compare the levels of pain experienced by the
different groups at the end of the drug treatment period. The researcher runs a Kruskal-Wallis H test
to compare this ordinal, dependent measure between the three drug treatments (i.e., the
independent variable) is the type of drug with more than two groups).
EXAMPLE 14:
The birth weight of an infant has been hypothesized to be associated with the smoking status of the
mother during the first trimester of pregnancy. The mothers are divided into four groups according
to smoking habit, and the sample of birth weights in pounds within each group is given as follows:
Group 1: (Mother is a nonsmoker)
Weight
7.5
6.9
7.4
9.2
8.3
7.6
Rank
19
14
18
24
23
20
118
Group 2: (Mother is an ex-smoker but not during the pregnancy)
Weight
5.8
7.1
8.2
7.1
7.8
Rank
6
15.5
22
15.5
21
80
Group 3: (Mother is a current smoker and smoke less than 1 pack per day)
Weight
5.9
6.2
5.8
4.7
7.2
6.2
Rank
8
10.5
6
1
17
10.5
53
Group 4: (Mother is a current smoker and smoke more than 1 pack per day)
Weight
6.2
6.8
5.7
4.9
6.2
5.8
5.4
Rank
10.5
13
4
2
10.5
6
3
49
EXAMPLE 15:
The effectiveness of advertising for two rival products (Brand X and Brand Y) was compared. Market
research at a local shopping centre was carried out, with the participants being shown adverts for
two rival brands of coffee, which they then rated on the overall likelihood of them buying the
product (out of 10, with 10 being "definitely going to buy the product"). Half of the participants gave
ratings for one of the products, the other half gave ratings for the other product.
EXAMPLE 16:
A random sample of eight drivers insured with a company and having similar auto insurance policies
was selected. The following table lists their driving experiences (in years) and monthly auto
insurance premiums.
Does the insurance premium depend on the driving experience or does the driving experience
depend on the insurance premium? Do you expect a positive or a negative relationship between
these two variables?
EXAMPLE 17:
Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact
cars, midsize cars, and full-size cars. It collects a sample of three for each of the treatments (cars
types). Using the hypothetical data provided below, test whether the mean pressure applied to the
driver’s head during a crash test is equal for each types of car. Use α = 5%.
EXAMPLE 18:
A farmer wants to know whether the weight of parsley plants is influenced by using a fertilizer. He
selects 90 plants and randomly divides them into three groups of 30 plants each. He applies a
biological fertilizer to the first group, a chemical fertilizer to the second group and no fertilizer at all
to the third group. After a month he weighs all plants. Can we conclude from these data that
fertilizer affects weight?
EXAMPLE 19:
Does region ‘say anything’ about marital status?
EXAMPLE 20:
A marketer believes that 4 smartphone brands are equally attractive. He asks 43 people which brand
they prefer. If the brands are really equally attractive, each brand should be chosen by roughly the
same number of respondents. In other words, the expected frequencies under the null hypothesis
are (43 cases / 4 brands =) 10.75 cases for each brand. The more the observed frequencies differ
from these expected frequencies, the less likely it is that the brands really are equally attractive.
Output as follows:
Interpret the findings.
EXAMPLE 21:
A scientist from Greenpeace believes that herrings in the North Sea don't grow as large as they used
to. It's well known that - on average - herrings should weigh 400 grams. The scientist catches and
weighs 40 herrings. Can we conclude from these data that the average herring weighs less than 400
grams?
EXAMPLE 22:
A marketer wants to know whether women spend the same amount of money on clothes as men.
She asks 30 male and 30 female respondents how much many rands they spend on clothing each
month. Do these data contradict the null hypothesis that men and women spend equal amounts of
money on clothing?
EXAMPLE 23:
A behavioural scientist wants to know whether drinking a single glass of beer affects reaction times.
She has 30 participants perform some tasks before and after having a beer and records their
reaction times. For each participant she calculates the average reaction time over tasks both before
and after the beer. Can we conclude from these data that a single beer affects reaction time?
EXAMPLE 24:
A policy maker wants to know whether age and nett monthly income are related in any way. She
asks 30 respondents. Do these data render it likely that age and income are related in the research
population?
EXAMPLE 25:
A company wants to know how job performance relates to IQ, motivation and social support. They
collect data on 60 employees.
EXAMPLE 26:
Comment on the following:
EXAMPLE 27:
18 respondents rated 3 commercials for cars on a percent (0 through 100 attractive) scale. We'd like
to know which commercial performs best in the population. So we'll first see if the mean ratings in
our sample are different. If so, the next question is if they're different enough to conclude that the
same holds for our population at large.
EXAMPLE 28:
Our data contain the result of a small experiment regarding creatine, a supplement that's popular
among body builders. These were divided into 3 groups: some didn't take any creatine, others took it
in the morning and still others took it in the evening. After doing so for a month, their weight gains
were measured. The basic research question is:
Does the average weight gain depend on the creatine condition to which people were assigned?
EXAMPLE 29:
The ratings of 3 car commercials by 18 respondents, balanced over gender and age category. Our
research question is whether men and women judge our commercials similarly. For each commercial
separately, our null hypothesis is:
“the mean ratings of men and women are equal.”
http://www.spss-tutorials.com/basics/
EXAMPLE 30
The mean Verbal SAT score for the population of first students at MANCOSA is 520. The standard
deviation of scores in this population is 95. An investigator believes that the mean Verbal SAT of first
year MBA students is significantly different from the mean score of the population. The mean of a
sample of 36 first years is 548.
Example 31:
An investigator predicts that individuals that fit the Type A Behaviour Pattern (highly competitive
and time conscious) will have higher scores on a questionnaire measure of need for achievement
that individuals that fit the Type B Behaviour pattern (absence of Type qualities). The investigator
collects need for achievement scores from 10 Type A subjects and 10 Type B subjects. Higher scores
reflect greater levels of need for achievement. Write the null and alternative hypotheses for testing
this prediction. Please use SPSS to test the null hypothesis stated above. Please provide a sentence
in APA format for a results section that states the conclusion the investigator is entitled to draw.
Group Statistics
Score
Type
Type A
Type B
N
10
10
Mean
11.2000
7.2000
Std. Deviation
2.69979
2.04396
Std. Error Mean
.85375
.64636
Test
Levene's Test for
Equality of
Variances
Score Equal variances
assumed
Equal variances
not assumed
F
.484
t-test for Equality of Means
Sig.
t
.495 3.735
3.735
df
Sig. (2Mean
Std. Error
tailed) Difference Difference
18
.002
4.00000
1.07083
16.766
.002
4.00000
1.07083
95% Confidence
Interval of the
Difference
Lower
Upper
1.75028 6.24972
1.73835
6.26165
EXAMPLE 32:
A researcher might want to test whether the average IQ score for a group of students differs from
100. Or a cereal manufacturer can take a sample of boxes from the production line and check
whether the mean weight of the samples differs from 1.3 pounds at the 95% confidence level.
EXAMPLE 33:
Comment on the above scatterplot, assuming the regression coefficient is 0.468, and p = 0.577
EXAMPLE 34:
A manufacturer of high-performance automobiles produces disc brakes that must measure 322
millimetres in diameter. Quality control randomly draws 16 discs made by each of eight production
machines and measures their diameters.
EXAMPLE 35:
A physician is evaluating a new diet for her patients with a family history of heart disease. To test the
effectiveness of this diet, 16 patients are placed on the diet for 6 months. Their weights and
triglyceride levels are measured before and after the study, and the physician wants to know if
either set of measurements has changed.
EXAMPLE 36:
An analyst at a department store wants to evaluate a recent credit card promotion. To this end, 500
cardholders were randomly selected. Half received an ad promoting a reduced interest rate on
purchases made over the next three months, and half received a standard seasonal ad.
EXAMPLE 37:
A sales manager wishes to determine the optimal number of product training days needed for new
employees. He has performance scores for three groups: employees with one, two, or three days of
training.
EXAMPLE 38:
In response to customer requests, an electronics firm is developing a new DVD player. Using a
prototype, the marketing team has collected focus group data. ANOVA is being used to discover if
consumers of various ages rated (between 0-100) the design differently.
EXAMPLE 40:
A grocery store chain surveyed a set of customers concerning their purchasing habits. Given the
survey results and how much each customer spent in the previous month, the store wants to see if
the frequency with which customers shop is related to the amount they spend in a month,
controlling for the gender of the customer.
Levene’s:
EXAMPLE 41:
In order to increase sales, motor vehicle design engineers want to focus their attention on aspects of
the vehicle that are important to customers--for example, how important is fuel efficiency with
respect to price willing to pay for vehicle. The output is as follows. Please state what you observe
from the table below.
EXAMPLE 42:
An automotive industry group keeps track of the sales for a variety of personal motor vehicles. In an
effort to be able to identify over- and underperforming models, you want to establish a relationship
between vehicle sales and vehicle characteristics (fuel efficiency, price, vehicle type, width, engine
size, fuel capacity, wheelbase, curb weight, horsepower).
EXAMPLE 43:
A hypothetical study of credit card usage follows each subject's monthly spending on their primary
card for two years, with spending broken out by the type of transaction (Grocery, Retail,
Entertainment, Travel, and Other). Each record in the dataset corresponds to given month of
spending and type of transaction, so the data collected for each subject requires 2 years × 12
months per year × 5 types of transactions = 120 records.
1. What nonparametric test can be used to test whether spending differs by primary card, you
can aggregate the records so that there is a single record for each subject that shows the
total spending for all 24 months over all 5 transaction types. Determine whether the total
spending differs by primary card.
2. Each transaction type is recorded for each subject, and is repeated within records for a given
subject. To use nonparametric tests to test whether spending differs by transaction type,
you can aggregate the records so that there is a record for each transaction type for each
subject that shows the total spending for all 24 months. Test whether spending differs by
transaction type.
EXAMPLE 44:
Determine the association between income level (categorised into low, medium and high) and PDA
(personal digital assistant) type owned (classified into the various brands). The test output is as
follows:
Interpret with reference to the scenario. Assuming the assumption of more than 5 counts in more
than 80% of the cells has has been met.