PSYC 510
Z T TESTS AND INGLE AMPLE S S -TESTS SSIGNMENT NSTRUCTIONS A I
OVERVIEW
This Homework: Z-Tests & Single Sample T-Tests Assignment is designed to assess your
understanding of the concepts and applications covered thus far in this course. This module
introduces two inferential tests – the test and single sample test; both of which are used to z t
determine whether a sample differs from a population. These tests are commonly used in
psychology, education, business, and other fields. This Homework: Z-Tests & Single Sample
T-Tests Assignment assesses your knowledge, skills, applications, and presentation of these tests
using professional conventions.
INSTRUCTIONS
Be sure you have reviewed this module’s before completing this Learn section Homework: Z-
Tests & Single Sample T-Tests Assignment. This Homework: Z-Tests & Single Sample T-
Tests Assignment is worth 60 points. Each question is worth 3 points. Six points are awarded for
mechanics/structure.
Part I contains general concepts from this module’s . Learn section
Part II requires use of SPSS. You will have to take screen shots and/or copy and paste from
your SPSS to place answers within this file. Make sure you only insert relevant and legible
images.
Part III is the cumulative section. These may include short answer and/or use of SPSS but
will review material from previous module(s).
Directions for each subsection are provided in the top of each table (in the blue shaded
areas).
Answers should be placed where indicated (wherever there is “ ”). ANSWER
Submit the file as a WORD document (.doc or .docx). Make sure the filename of your
submission includes your full name, course and section.
oExample: HW6_JohnDoe_510B01
Make sure to check the before beginning this Homework Grading Rubric Homework: Z-Tests
& Single Sample T-Tests Assignment.
Part I: General Concepts
These questions are based on the concepts covered in this
module’s assigned readings and presentations.
Answer the following questions using your own words.
1. What is the critical value for a one-tailed test? For a two-tailed test? Which is more likely to z z
result in a rejection of the null hypothesis? Why?
For a one-tailed or directional test, it will always be 1.645. For a two-tailed or non-directional test, the
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PSYC 510
critical value will always be a 1.96. If the z obtained value falls in the rejection region, you get to reject
the null hypothesis. The rejection region
Since the result of the one-tailed z test is approximately half that of the two-tailed z test, it is more likely
to reject the null hypothesis.
2. Why does Change when the sample size changes? What must be computed to determine tcv. tcv.?
The critical values represent the rejoining of the rejection changes for samples of various sizes, while the
tcv changes are caused by variations in sample distribution sizes. An unbiased estimator for the
population's standard deviation, an estimated standard error, and the degrees of freedom must be
computed in order to determine the value of tev.
3. Henry performed a two-tailed test for an experiment in which = 24. He could not find his N
table of critical values, but he remembered the at df = 13. He decided to compare his t tcv tobt
with this . Is he more likely to make a Type I or a type II error in this situation? Briefly tcv
discuss why.
Henry is likely to commit a Type II error in this case. This error will likely occur when a false H0 occurs
and the same is not rejected because the difference was overlooked.
Given a population standard deviation of 12, answer the following two questions.
4) Calculate the standard error of
the mean ( given the following
two sample sizes (show all your
work and round to two decimal
places):
N1 = 20
N2 = 70
N1 =
N2 =
N1 = 2.68
N2 = 1.43
5) How does the sample size
change the standard error of the
mean? What does this mean for
statistical power?
The two are inversely correlated, meaning that a larger
sample size results in a smaller standard error of the mean.
This factor strengthens the statistical power in respect to the
statistical power.
Calculate the critical degrees of freedom and identify the critical values for the following tests,
using = .05 and the tables in your e-book for all scenarios (do NOT round). Then, state whether p
the null hypothesis would be rejected or failed to be rejected.
6) Single sample test: t-
two-tailed, N = 20, =t
2.05
df= 19 critical = 2.093 Reject or Fail to Reject H : to
Fail to be rejected.
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PSYC 510
7) Single sample t-test:
one-tailed, N = 20, = t
2.05
df=19 critical =1.729 Reject or Fail to Reject H : to
Reject
8) Pearson’s r
correlation: two-tailed,
N = 15, = 0.47r
Df=13 critical = .5139 Reject or Fail to Reject H : to
Fail to be rejected.
9) Pearson’s r
correlation: one-tailed,
N = 15, = 0.47r
df=14 critical =.4409 Reject or Fail to Reject H : ro
Reject
A company decides to offer a monetary incentive for employees who log a specified
number of hours spent exercising in an attempt to employee health. The average improve
health score (higher = better) of the 75 employees who logged enough hours was 87. The
mean health score for all employees (population) was 85, with a population standard
deviation of 6.5.
10) Calculate the standard error of the mean.
.75
11) Conduct the z-test. Show your work (use
at least two decimal places throughout).
What is the z score? z
obt obt = 2.76
12) Write your conclusion using complete
sentences in APA format. Don’t forget to
include the statistical statement and whether
you reject or fail to reject the null hypothesis.
According to the z test, the average health
scores were significantly higher than the
population, [Z(N = 75) = 2.67; p<.05 (one-
tailed)]. The null hypothesis is then rejected
in this situation.
Part II: SPSS Application
These questions require the use of SPSS. Remember you must
submit all of your work within this word document. You will need
to take a screen shot of your data view if necessary, or copy and
paste your output into the spaces below. Remember to report the
exact p value provided by SPSS output – simply reporting p<.05 or
p>.05 is not acceptable (unless SPSS output states p=.000 – in
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PSYC 510
that case you can report p<.001).
Exercise 1
Spatial ability was quantified using a sample of the general population (N=15). Their
scores are shown below, where higher scores represent better spatial ability. Enter this
data into SPSS to answer the following questions.
52 59 63 65 58
55 62 63 53 59
57 61 60 59 57
13)
Run descriptive statistics for general population data provided above (make sure
to include the mean and confidence interval by using the “Explore” option as
shown in this module’s presentation).
14)
You want to compare your sample of the general population to individuals who
listen to classical music, but you only know their mean ( = 60). Run a single
sample test. Paste the output below. t
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PSYC 510
Answer under One-Sample Test portion
15)
Write a results section in current APA style describing the outcome.
All homework results sections must follow the example given in the SPSS
presentation and in the textbook. Results sections are multiple sentences (a
single paragraph) and must include the APA-formatted statistical statement and
a decision about the null hypothesis.
A single sample t-Test was used to compare how individuals who listened to classical music
had spatial abilities that differed from the population mean of 60. The sample and population
mean is 60, [t(14) = -1.186, p = .255 (two tailed)]. The sample scores, excluding the mean for
the total population, ranged between 56.82 and 60.91 at a 95% confidence level. Therefore, the
decision should be to reject the null hypothesis.
Part III: Cumulative
These questions can be related to anything covered thus far in the
course.
A recruiter wants to know if college GPA is truly predictive of one’s grit. He examined this by
having 14 job applicants complete a grit inventory using a Likert scale (range 1 -7) where
higher numbers indicate more “grit”. GPA was confirmed using college transcripts (scale 0 –
4.0). Enter the data shown below into SPSS to assess whether GPA can predict one’s grit.
Remember – prediction requires a different analysis than mere relationships. Choose the
correct test to analyze this question, set up the SPSS file, and run the analysis. Paste the
output, appropriate graph, and then report the results using complete sentences in APA style
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PSYC 510
following the example in the lecture presentation for this statistical test.
Grit GPA
6.5 4.0
4.0 3.1
3.7 2.7
5.8 3.5
4.7 3.1
5.5 3.3
3.9 2.7
1.1 2.8
3.5 3.1
2.7 2.6
5.1 3.8
3.2 2.2
5.6 2.8
6.1 2.5
16) Paste appropriate SPSS output.
17) Paste appropriate SPSS graph.
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PSYC 510
18) Write a Results section in current APA style describing the outcome using complete
sentences. Make sure you report the statistical notation in APA format and include all
relevant information.
A linear regression analysis was performed to assess the prediction if college GPA can predict
one’s grit and was found insignificant.
F 1,12) = 4.510, p=3.15
The regression equation for predicting Grit is Y = 1.556 X-.306 (Y=1.56 X=.31)
The correlation between GPA and GRIT is .523.
The linear relationship between the GPA and GRIT accounted for 27% of the variation.
Submit this assignment by 11:59 p.m. (ET) on Sunday of Module 6. Remember to name the file
appropriately.
Done!
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