Assignment #10: One Sample t Tests
(15 points)
Due END OF DAY, Week 10 lab (11/4/2020)
In many situations, we may want to determine whether our sample is representative of a broader, more general
population, or if it is “special” in some way. In these cases, we test our hypotheses using one-sample t tests.
In this week’s lab, you will practice using the t statistic to perform a series of hypothesis tests, both by hand and
using SPSS. For each hypothesis test, you will start by stating null and alternative hypotheses, continue by
performing calculations OR interpreting SPSS output, and then conclude by writing the results of the tests using
APA format.
Instructions:
Work through the tasks on the following pages.
oTasks 1-3 should be completed individually.
oTask 4 may be completed with your group.
oExtra credit (3 points): For additional practice, complete Exercise 5.1 (pp. 161-162) in the
Student Study Guide. Answer the questions, and write the results of the hypothesis test. This
exercise must be completed individually.
Be sure to show all work for your hand calculations, as appropriate. This includes showing the formula,
substitution of numbers into the formula, and final answer. You will need to turn in your hand
calculations with your assignment. Scan in any written work and include it with your submission.
Save your SPSS output. “Copy special” your output tables (as picture files), and then paste them into a
Word document.
Using your calculations and SPSS output, write interpretation sentences that incorporate statistics,
following the examples we did in class.
Submit all work through the drop box in eCampus. A single document is preferred, but multiple files will
be accepted.
NOTES:
As you work through the SPSS exercises on the following pages, DO NOT CLOSE THE OUTPUT WINDOW,
or you will lose your work. You may want to SAVE your output intermittently.
Name: __________________________ Fall 2018
Section:_______ PSYC 203
Task 1: Perform a One-Sample t Test from Summary Data
A professor wants to determine whether the leaders of campus clubs have different GPAs than the
average GPA of 2.8 for the university. Forty students who lead campus clubs were found to have an
average GPA of 3.12 with a standard deviation of 0.6. Use an alpha of .01 to test the null hypothesis.
Step 1. State the hypotheses (in words and using symbols).
Step 2. Identify the information.
Population mean =
Sample mean =
Sample standard deviation =
Sample size =
Step 3. Calculate standard error of the mean and the t statistic.
Step 4. Find critical values based on alpha level and degrees of freedom.
=
df = n – 1 =
Critical value(s) =
Step 5. Calculate and interpret the effect size.
Interpretation?
Step 6. Write the results (APA format).
S
M
=S
n=
t=M-
m
S
M
=
Cohen's d=M-
m
S=
Name: __________________________ Fall 2018
Section:_______ PSYC 203
Task 2: Perform a One-Sample t Test from Raw Data
A health psychologist believes that fraternity members consume more alcohol than the general campus
population. Prior research has shown college men consume an average of 3.3 drinks per week. The
professor surveyed fraternity members regarding their drinking; the data obtained appear below. Does
the alcohol consumption of fraternity members differ from the general student population? Use an
alpha of .05 to test the null hypothesis
Step 1. State the hypotheses (in words and using symbols).
Step 2. Calculate sample mean and standard deviation.
Drinks per week Difference Squared Difference (Deviation)
X
MX -
2
)( MX -
5
2
0
8
10
6
1
9
7
0
X=
=- 0)( MX
Always…within
=- 2
)( MX
rounding!
M=∑X
n=¿
S2=∑
(
X−M
)
2
n−1=¿
Name: __________________________ Fall 2018
Section:_______ PSYC 203
S=
√
S2=¿
Step 3. Calculate standard error of the mean and the t statistic.
Step 4. Find critical values based on alpha level and degrees of freedom.
=
df = n – 1 =
Critical value(s) =
Step 5. Calculate and interpret the effect size.
Interpretation?
Step 6. Write the results (APA format).
S
M
=S
n=
t=M-
m
S
M
=
Cohen's d=M-
m
S=
Name: __________________________ Fall 2018
Section:_______ PSYC 203
Task 3: Perform One-Sample t Tests Using SPSS
A school nurse obtained the heights and weights of 6th grade children in a low-income neighborhood to
determine whether these children differ in height or weight from the national averages for children their age.
Nationally, 6th grade children have an average height of 56 inches and weigh an average of 75 lbs. Use SPSS to
conduct tests of the null hypotheses; use an alpha of .05 for each test.
Height Hypothesis
Step 1. State the hypotheses for height (in words and using symbols).
Step 2. Analyze the data in SPSS, and examine the output.
Download the data file (Asst10-Data.sav) from the Assignment 10 folder on eCampus.
Open SPSS Statistics. Go to File Open and select the file you’ve downloaded.
To test the null hypothesis for Height...
oClick on Analyze Compare Means One-Sample T Test…
oSelect Weight and click the arrow beside Test Variable(s).
oEnter 56 (the null hypothesis value) in the Test Value box, and then click OK.
Is significance less than ? YES NO
Results ARE / ARE NOT statistically significant.
Step 3. Calculate and interpret the effect size.
Cohen's d=M-
m
S=
Name: __________________________ Fall 2018
Section:_______ PSYC 203
Interpretation:
Weight Hypothesis
Step 1. State the hypotheses for weight (in words and using symbols).
Step 2. Analyze the data in SPSS, and examine the output.
Using the procedure outlined above, test the null hypothesis for Weight (be sure to use the correct test
value).
Is significance less than ? YES NO
Results ARE / ARE NOT statistically significant.
Step 3. Calculate and interpret the effect size.
Interpretation:
BOTH HYPOTHESES:
Summarize the descriptive statistics and hypothesis test results, as if writing the results section of an
APA style paper.
Cohen's d=M-
m
S=
Name: __________________________ Fall 2018
Section:_______ PSYC 203
Task 4: Perform One-Sample t Tests on PROJECT Data Using SPSS
The standardized scales used for your studies have been tested and validated by previous researchers. Expected
scores (i.e., population means) on the scales are as follows:
Big Five Personality: 50th percentile (all subscales, by definition)
Perceived Stress Scale: 23.42 (based on two student samples; Cohen, Kamarck, & Mermelstein, 1983)
Rosenberg Self-Esteem Scale: 22.12 (based on a student sample; Martín-Albo, Núñez, Navarro, &
Grijalvo, 2007)
Do students in our class differ from these expectations? Using the “cleaned up” data set you created last week,
test the null hypothesis ( = .05) for the standardized scale you’re using in your study.
Step 1. State the hypotheses (in words and using symbols).
Step 2. Analyze the data in SPSS, and examine the output.
Using the procedure outlined above, test the null hypothesis (be sure to use the correct test value).
Is significance less than ? YES NO
Results ARE / ARE NOT statistically significant.
Step 3. Calculate and interpret the effect size.
Interpretation:
Step 4. Write a sentence summarizing the results of hypothesis test. (NOTE: You may want to integrate
this into the Results section of your paper!)
Cohen's d=M-
m
S=
Name: __________________________ Fall 2018
Section:_______ PSYC 203
=
*** Don’t forget to turn in your SPSS output with your assignment! ***
Extra Credit (up to 3 points)
Complete Exercise 5.1 (pp. 161-162) in the Student Study Guide. Answer the questions (reproduced below), and
write the results of the hypothesis test.
Based on the table shown in SPSS, state the following values for the sample:
Sample size ________
Sample mean ________
Sample standard deviation ________
Estimated standard error ________ (labeled “Std. Error Mean”)
Based on the table shown in SPSS, state the following values associated with the test statistic:
Mean difference ________ (This is the numerator for the test statistic.)
t obtained (t) ________
Degrees of freedom (df) ________
Significance (two-tailed) ________
Based on the value of the test statistic, what is the decision for a one-sample t test? (Circle one)
Not significant Significant
Compute Cohen’s d (show your work) and state the size of the effect as small, medium, or large. In a
sentence, also state the number of standard deviations that scores shifted in the population.
Write the results (in APA format).
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