Homework 6

Percentiles and Hypothesis Testing with Z-Tests

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.

2) Using the z table in Appendix B, calculate the following percentages for a z score of -0.45

2-a) % above this z score: Answer

Work:

2-b) % below this z score: Answer

Work:

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

Answer

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 Answer

4b) z = -0.97 Answer

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 general population? Answer

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.

Answer

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.

Answer

7) For the following scenario, state the null and research hypotheses in both words and symbolic notation. Symbolic notation must include the symbols “ m 1 ” and “ m 2 ” and a comparison operator (=, , <, >, , ), as described in Nolan and 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 (H 0 ): Symbolic Notation

Answer

Null Hypothesis:

Written Statement

Answer

Research Hypothesis (H 1 ): Symbolic Notation

Answer

Research Hypothesis:

Written Statement

Answer

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 ( m = 71 in.) with s = 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.

10a)

What is the z score for an officer who is 72 inches tall? Based on the z score and the z table, what is the officer’s percentile ? (Hint: See slide 7 of this week’s related presentation)

Answer (z score): Work (required):

Answer (percentile):

Work/reasoning using z table (required):

10b) What is the height (in inches) that marks the 80 th percentile for this group of officers? (Hint: See slides 14-16 of this week’s related presentation)

Answer

Work (required):

10c)

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

Answer Work (required):

Part I: Questions 11a-11c

The verbal part of the Graduate Record Exam (GRE) has a m of 500 and s = 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.

11a) What is the z score for a GRE score of 583?

What is the percentile rank of this z score? (Hint: See slide 7 of this week’s related presentation)

Answer (z score):

Work (required):

Answer (percentile):

Work (required):

11b)

What GRE score corresponds to a percentile rank of 25%? (Hint: See slide 17 of this week’s related presentation)

Answer

Work (required):

11c)

If you wanted to select only students at or above the 82 nd percentile, what GRE 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)

Answer

Work (required):

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:

1)

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

Answer

Work:

2)

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

Answer

Work:

3)

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

Answer

Work:

4)

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

Answer

Work: