1. A fitness instructor wants to use scores on a standardized physical endurance assessment (max scoreof 100) to assess the effectiveness of his exercise program. In a sample (N = 49) of people who have
completed his exercise program, the mean endurance score is 74 points (M= 74). In the general
population of gym-goers, the mean is μ= 72 points, with a standard deviation of σ = 7 points. Based on
these data, do people who complete the exercise program have higher physical endurance than the
general population of gym-goers?
a. What type of statistical test do you need to perform? How do you know? (1pt)
b. Write the null and alternative hypotheses (2-tailed) in words (1 pt) and symbols (1 pt) (2 pts total)
c. What is the critical value that your test statistic must exceed? (2-tailed, α = .05) (1 pt)
d. Calculate the test statistic (2 pts)
e. Make a decision: reject or retain the null hypothesis? (1 pt)
f. Interpret what this result means in a concise sentence (i.e., answer the research question). (2 pts)
g. Calculate the upper and lower bounds of the 95% confidence interval (2pts)
95% CI: [ , ]
2. Week 4 of the Spring 2023 semester (the week of our first exam) was very cold. For those 5 weekdays
(Mon-Fri), the mean daily temperature was 2.41° F. Mankato’s historical mean for Week 4 of the spring
semester is 16.62° F, with unknown standard deviation. Was the mean temperature of Week 4 this year
significantly colder than the historical (population) mean?
a. What type of statistical test do you need to perform? How do you know? (1 pt)
b. Find the degrees of freedom (df) and use it to find the critical value (2-tailed, α = .05) (1 pt total).
(0.5 pt) df =
(0.5 pt) Critical value =
c. Calculate your test statistic. Use data below. Show work (5 pts).
day
monday
tuesday
wednesday
thursday
friday
Temperature (*F) X
-2.58
1.75
11.04
6.33
-4.50
M=2.41
X-M
(X-M)²
E(X-M)²=
d. Make a decision: reject or retain the null hypothesis? (1 pt).
e. Interpret what this result means in a concise sentence (i.e., answer the research question). (2 pts)
3. Xtreme Supplements Company has been losing money lately and wants to do something to boost
their sales. They decide to run a new promotion called the SWOLE Challenge, in which they have people
work out for two months while using their Xtreme BULK protein powder, to assess effectiveness, each
participant’s strength is measured before and after the SWOLE challenge.
The table below summarizes data from a sample (N = 8) of people who completed the challenge.
Strength was measured via a variety of methods, yielding a composite strength score (measured on a 0100 scale). Based on these data, is strength significantly greater after the SWOLE challenge vs before?
a) What type of statistical test do you need to perform? How do you know? (1 pt)
b) Write the null and alternative hypotheses (2-tailed) in words (1pt) and symbols (1pt) (2 pts total).
c) Find the degrees of freedom (df) and use it to find the critical value (2-tailed, α = .05) (1 pt total).
(0.5 pt) df =
(0.5 pt) Critical value =
d) Complete the table below and calculate the test statistic (6 pts)
Person#
1
Strength
before swole
challenge
23
Strength after
swole
challenge
40
2
18
32
3
45
55
4
14
30
5
58
68
6
32
44
7
65
70
8
20
42
e) Make a decision: reject or retain H0? (1 pt).
f) Interpret what this result means in a concise sentence (i.e., answer the research question). (2 pts)
g) Calculate a 95% confidence interval around the mean difference (2 pts). 95% CI: [ , ]
h) Write a concise sentence describing what the 95% CI tells you (2 pts).
i) Calculate effect size using Cohen’s d (2 pts)
j) Write a concise sentence describing what this Cohen’s d value means. (note: don’t answer by labeling
it as a small/medium/large effect). (2 pts).
