PRACTICE QUESTIONS
Applied Statistics-II
Chi-Square (goodness of fit test)
1. In a psychological experiment, a subject guesses the color of cards being drawn from a
deck. There are only two-color options: red or black. Out of 80 guesses, the subject
correctly identifies the color 48 times. Use the Chi-square goodness of fit test to determine
whether this performance differs significantly from chance at the 0.05 significance level.
(Answer: 3.2)
2. After losing a board game, your friend believes she might have lost because of a problem
with your dice. To find out, she rolls your dice 60 times and obtains the following
frequencies:
Number 1 2 3 4 5 6
Frequency 8 11 6 9 12 14
Should she reject the null hypothesis that the dice lands on each number with equal
probability? (Answer: 4.2)
3. You work at a nut factory and you’re in charge of quality control. The nut factory produces
a nut mix that’s supposed to be 50% peanuts, 30% cashews, and 20% almonds. To check
that the nut mix proportions are acceptable, you randomly sample 1000 nuts and find the
following frequencies:
Nut Peanuts Cashews Almonds
Frequency 621 189 190
Should you reject the null hypothesis that the nut mix has the desired proportions of nuts?
(Answer: 70.85)
Chi-square (Test of Independence)
1. A dog trainer wants to know if golden retrievers and French bulldogs are equally good at
learning how to skateboard. She tries to train 40 golden retrievers and 60 French bulldogs
to skateboard and finds the following:
Skateboards Can’t skateboard
Golden retrievers 20 20
French bulldogs 50 10
Should she reject the null hypothesis that the dog’s breed is unrelated to their skateboarding
ability? (Answer: 12.7)
2. A restaurant reviewer wants to know if three popular burger restaurants are equally
recommended by their customers. At each of the three restaurants, he asks 25 random
customers whether they would recommend the restaurant to a friend. He finds the
following:
Would recommend Would not recommend
Tasty Burgers 20 5
Burger Prince 22 3
Burger Town 18 7
Should he reject the null hypothesis that the proportion of customers recommending the
restaurant is the same for the three restaurants? (Answer: 2)
ANOVA
1. A study of depression and exercise was conducted. Four groups were used. A depression
rating was given to members in each group. Small random samples from each groups
provided the following data:
Cycle Group 63 58 61
Sedentary Group 71 64 68
Runners 49 52 47
Walkers 45 43 49
Use ANOVA to test if the mean depression ratings for the four groups are different. Use α
= .05. (Answer: 4.07)
2. A research study was conducted to examine the clinical efficacy of a new antidepressant.
Depressed patients were randomly assigned to one of three groups. After four weeks of
treatment, the patients completed the Beck Depression Inventory.
Placebo Low Dose Moderate Dose
38 22 14
47 19 26
39 8 11
25 23 18
42 31 5
Is there a significant difference between the groups? (Answer: 11.26)
3. Neuroscience researchers examined the impact of environment on rat development. Rats
were randomly assigned to be raised in one of the four test conditions. After two months,
the rats were tested on a variety of learning measures, and several neurological measure.
The data for the maze task is below:
Impoverished Standard Enriched Super Enriched
22 17 12 8
19 21 14 7
15 15 11 10
24 12 9 9
18 19 15 12
Are there any significant differences between the 4 testing conditions? (Answer: 12.71)
Sign Test (Single sample)
1. A student tells her parents that the median rental rate for a studio apartment in Portland is
$700. Her parents are skeptical and believe the rent is different. A random sample of studio
rentals is taken from the internet; prices are listed below. Test the claim that there is a
difference using αα = 0.10. Should the parents believe their daughter?
700, 650, 800, 975, 855, 785, 759, 640, 950, 715, 825, 980, 895, 1025, 850, 915, 740, 985,
770, 785, 700, 925
2. A professor believes that a new online learning curriculum is increasing the median final
exam score from the previous year, which was 75. A random sample of final exam scores
were collected for students that went through the new curriculum. Test to see if the new
curriculum is effective using α=0.05.
78, 100, 75, 64, 87, 80, 72, 91, 89, 70, 82, 76
Sign Test (Paired samples)
1. We have the following data on number of ear infections on swimmers before and after
taking a medication that is hypothesized to prevent infections:
Swimmer Infections before Infections after
A 3 2
B 0 1
C 5 4
D 4 0
E 2 1
F 4 3
G 3 1
H 2 2
I 1 3
2. The table below shows the times taken by a random sample of people to perform a simple
task on their first and second attempts. Test, at the 5% significance level, whether most
people take less time on the second attempt than on the first attempt:
Person A B C D E F G H
1st Attempt 6.3 3.5 7.1 3.7 8.4 3.9 4.7 5.2
2nd Attempt 5.1 3.4 6.2 4.5 7.3 4.0 3.6 5.1
Mann-Whitney U Test
1. 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. Half of the participants gave ratings for one of the products,
the other half gave ratings for the other product.
Brand X Brand Y
Group 1 Ratings Group 2 Ratings
1 3 1 9
2 4 2 7
3 2 3 5
4 6 4 10
5 2 5 6
6 5 6 8
(Answer:2)
2. Consider a randomized controlled trial evaluating a new anti-retroviral therapy for HIV. A
pilot trial randomly assigned participants to either the treated or untreated groups. Use
Mann-Whitney test to assess the viral load in the treated versus the untreated groups.
Treated 540 670 1000 960 1200 4650 4200
Untreated 5000 4200 1300 900 7400 4500 7500
(Answer: 8)
3. Researchers have asked several smokers how many cigarettes they had smoked in the
previous day. Here are the data.
Women Men
4 2
7 2
10 5
15 6
10 8
5 16
The distribution that these data are drawn from is not normal. Is there a difference between
number of cigarettes smoked per day between the genders?
4. A researcher wants to compare the effectiveness of two different diets on weight loss. After
six weeks, their weight loss (in pounds) was recorded for each participant.
Group A 4 10 8 11 7 9 12 12 8 16
Group B 11 7 13 5 13 14 10 5 14 6
Wilcoxon Signed Rank Test
1. In order to investigate whether adults report verbally presented material more accurately
from their right than from their left ear, a dichotic listening task was carried out. Number
of words reported:
Participant Left ear Right ear
1 25 32
2 29 30
3 10 8
4 31 32
5 27 20
6 24 32
7 26 27
8 29 30
9 30 32
10 32 32
11 20 30
12 5 32
2. A coach is interested in determining if his new training program will improve his athletes
400-meter sprint time. He obtains the record of 7 athletes both before and after his new
training program which are shown below.
Athlete Before After
1 63 58
2 61 57
3 62 59
4 58 57
5 59 58
6 56 55
7 61 55
According to a Wilcoxon signed-ranks test, at a 5% significance level, do these scores
provide evidence of an increase in median sprint time?
3. A pharmaceutical company claims they have developed a modern blood pressure
medication that has minimal side effects. Shown below are the participants blood pressure
before and after taking the medication for 8 weeks.
Participant BP-Before BP-After
1 122 118
2 132 130
3 125 127
4 127 127
5 136 130
6 128 135
7 131 124
8 129 126
Using a Wilcoxon signed-ranks test, do these scores provide evidence of a decrease in
median blood pressure?
