PSYC 354  Homework 6 Solution

PSYC 354

HOMEWORK 6
Percentiles and Hypothesis Testing with Z-Tests
When submitting this file, be sure the filename includes your full name, course and section.
Example: HW6_JohnDoe_354B01
Be sure you have reviewed this module/week’s lesson and presentations along with the practice
data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, then
copy and paste your output and graphs into your homework document file. Answer any written
questions (such as the text-based questions or the APA Participants section) in the appropriate
place within the same file.

Part I: Concepts
Questions 1–4
These questions are based on the Nolan and Heinzen reading and
end-of-chapter questions.

Part I: Questions 1-7
End-of-chapter problems:

Answer the following questions.
If applicable, remember to show work in your homework document for partial credit.

1) What are the 6 steps of hypothesis testing?
(State the 6 steps)
A)
B)
C)
D)
E)
F)
2) Using the z table in Appendix B, calculate the following percentages for a z score of
-0.45
2-a) % above this z
2-b) % below this z

Work:
Work:

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2-c) At least as extreme
as this z score (on either
side):

Work:

3) Rewrite each of the following percentages as probabilities, or p levels:
3-a) 5% = Answer
3-b) 95% = Answer
3-c) 43% = Answer
4) If the critical values, or cutoffs, for a two-tailed z test are -2.05 and +2.05, determine
whether you would reject or fail to reject the null hypothesis in each of the following
cases:
4a) z = 2.23
4b) z = -0.97
5)

Imagine a class of twenty-five 12-year-old girls with an average height of 62 inches.
We know that the population mean and standard deviation for this age group of
girls is m=59 inches, s = 1.5 inches. (Note that this is a z statistic problem.)

5a) Calculate the z statistic for this sample (not the z score). Answer
5b) How does this sample mean compare to the distribution of sample means? In other
words, how does the height of the girls in the sample compare to the height of girls in th
6)

For the following scenarios, identify whether the researcher has expressed a
directional or a nondirectional hypothesis:

6a) Social media has changed the levels of closeness in long-distance relationships.
6b) A professor wonders whether students who eat a healthy breakfast score better on
exams in morning courses than those who do not eat a healthy breakfast.
For the following scenario, state the null and research hypotheses in both words and
symbolic notation. Symbolic notation must include the symbols “ ” and “ ” and a
comparison operator (=, ≠ , &lt;, &gt;, ≤ , ≥ ), as described in Nolan and
7)

Heinzen (2014). Remember to consider whether the hypothesis is nondirectional or
directional.
Scenario: A professor wonders whether students who eat a healthy breakfast score
better on exams in morning courses than those who do not eat a healthy breakfast.

Null Hypothesis (H0): Symbolic
Notation

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Null Hypothesis:

Written Statement
Research Hypothesis (H1): Symbolic
Notation
Research Hypothesis:
Written Statement

Part I: Questions 8a-8g
Fill in the highlighted blanks with the best word or words.

8-a) Values of a test statistic beyond which you reject the null hypothesis are called
________.

8-b)

The ________ is the area in the tails in which the null can be rejected.
The probability used to determine the critical values, or cutoffs, in hypothesis testing

8-c) is known as a ________ level, also known as alpha.

If your data differ from what you would expect if chance were the only thing

8-d) operating, you would call your finding ________.

8-e) A hypothesis test in which the research hypothesis is directional is a(n) ________ test.
8-f)

A hypothesis test in which the research hypothesis specifies that there will be a
difference but does not specify the direction of that difference is a(n) ________ test.

8-g) If your z-statistic exceeds the critical cutoff, you can ________ the null hypothesis.

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Part I: Questions 10a-10c
The police department of a major city has found
that the average height of their 1,200 officers is
71 inches (in.) with = 2.6 inches. Use
the normal distribution and the formulas and
steps in this week’s presentations to answer the
following questions:
Note: Showing work is required for this section. Remember that it helps to transfer the raw
mean and SD from the description above to the standardized curve shown here (though you
don’t need to show this). This helps compare raw and z scores and check your work.
What is the z score for an officer who is 72 inches tall? Based on the z score and
10a) the z table, what is the officer’s percentile? (Hint: See slide 7 of this week’s related
presentation)
Work (required):
score):
Work/reasoning using z table (required):
(percentile):

10b
)

What is the height (in inches) that marks the 80th percentile for this group of
officers? (Hint: See slides 14-16 of this week’s related presentation)

Work (required):

10c) What percent of officers are between 68 and 72 inches tall? (Hint: See slide 12 of
this week’s related presentation)
Work (required):

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Part I: Questions 11a-11c
The verbal part of the Graduate Record Exam
(GRE) has a of 500 and = 100. Use the
normal distribution and the formulas and steps in
this week’s presentations to answer the
following questions:
Note: Showing work is required for this
section. Remember that it helps to transfer the raw mean and SD from the description above to
the standardized curve shown here (though you don’t need to show this). This helps compare
raw and z scores and check your work.
What is the z score for a GRE score of 583?

11a) What is the percentile rank of this z score? (Hint: See slide 7 of this week’s related
presentation)
Work (required):
score):
Work (required):
(percentile):
What GRE score corresponds to a percentile rank of 25%? (Hint: See slide 17 of
11b) this week’s related presentation)

Work (required):

If you wanted to select only students at or above the 82nd percentile, what GRE
11c) score would you use as a cutoff score (i.e. what GRE score corresponds to this
percentile)? (Hint: See slides 14-16 of this week’s related presentation)
Work (required):

Part II: SPSS Analysis
For this section, you will be using last module/week’s data set containing IQ
scores.
Open the file; it should also contain the standardized IQ variable you created
last module/week.

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Part II:
Question 1a &amp; 1b
Use last week’s HW file that you created using IQ scores, and the SPSS reading and
presentation from this week.
Using the z-scored IQ variable, create percentile ranks assuming the scores are
normally distributed.
o Call the new percentile variable “IQ rank.”

1a)

List the first 5 IQ ranks from your file (rows 1–5).

Row 1:
Row 2:
Row 3:
Row 4:
Row 5:

1b
)

Which raw IQ score seems to best divide the top 50% from the bottom 50% of
scores?
(This score can be found by looking carefully over the values in the IQ rank column)

Part III: SPSS Data Entry and Analysis
There is no Part III material this module/week.

Part IV: Cumulative
Data provided below for respective questions.

Part IV: (Non-SPSS)
Questions 1-4
For a distribution with M = 40 and s = 5:

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1)

What is the z-score corresponding to a raw score of 32?

2)

What is the z-score corresponding to a raw score of 50?

3)

Work:

If a person has a z-score of 1.8, what is his/her raw score?

4)

Work:

Work:

If a person has a z-score of -.63, what is his/her raw score?

Work:

Part IV: (Non-SPSS)
Question 5-8
For the following types of data, state the graph that would be the best choice to display
the data.
Two items have more than one correct answer—for these, either answer is acceptable.

5)

A nominal independent variable (IV) and a scale dependent variable (DV)

6)

One scale variable with frequencies (when you want to see the general shape of
the distribution).

7)

One scale IV and one scale DV