PSYC354 HOMEWORK 6

Homework 6

Percentiles and Hypothesis Testing with Z-Tests

Be sure you have reviewed this module/week’s lessons and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, and then copy and paste your output and graphs into your homework document file. Number all responses. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file. Review the “Homework Instructions: General” document for an example of how homework assignments must look.

Part I: Concepts

For this module/week, this section comprises most of your assignment. For help working the percentile and z-score problems, refer to the presentations in this module/week on z-tables and percentages as well as hypothesis testing with z-tests.

1. Answer the following Nolan and Heinzen end-of-chapter questions for Chapter 7: 7.8, 7.18, 7.20, 7.22, 7.28 [sections (a) and (b)], 7.32 [sections (a)–(e)], 7.34, 7.39, and 7.40 [sections (a) and (b)]. If applicable, remember to show work in your homework document for partial credit.

7.8 What are the six steps of hypothesis testing?

7.18 Using the z table in Appendix B, calculate the following

percentages for a z score of ?0.08:

a. Above this z score

b. Below this z score

c. At least as extreme as this z score

0.97 a. 33.25 b. 33.55 33.40 c. 33.397 and 33.403

0.98 a. 33.486 b. 33.814 33.65 c. 33.648 and 33.652

0.99 a. 33.704 b. 34.076 33.89 c. 33.889 and 33.891

1.00 a. 33.57 b. 34.69 34.13 c. 34.13 and 34.13

1.01 a. 33.82 b. 34.94 34.38 c. 34.381 and 34.379

7.20 Rewrite each of the following percentages as probabilities, or p levels:

a. 5%

b. 83%

c. 51%

7.22 If the critical values for a hypothesis test occur where 2.5% of the distribution is in each tail, what are the cutoffs for z?

7.28 If the cutoffs for a z test are -2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases:

a.

b.

c. A z score for which 49.6% of the data fall between z and the mean

7.32 z distribution and height: Elena, a 15-year-old girl, is 58 inches tall. Based on what we know, the average height for girls at this age is 63.80 inches, with a standard deviation of 2.66 inches.

a. Calculate her z score.

b. What percentage of girls are taller than Elena?

c. What percentage of girls are shorter?

d. How much would she have to grow to be perfectly average?

e. If Sarah is in the 75^th percentile for height at age 15, how tall is she? And how does she compare to Elena?

7.34 The z statistic and height: Imagine a class of thirty-three 15-year-old girls with an average height of 62.6 inches. Remember, u= 63.8 inches and o=2.66 inches.

a. Calculate the z statistic.

b. How does this sample of girls compare to the distribution of sample means?

c. What is the percentile rank for this sample?

7.39 Directional versus nondirectional hypotheses: For each of the following examples, identify whether the research has expressed a directional or a nondirectional hypothesis:

A. A researcher is interested in studying the relation between the use of antibacterial products and the dryness of people’s skin. He thinks these products might alter the moisture in skin compared to other products that are not antibacterial.

B. A student wonders if grades in a class are in any way related to where a student sits in the classroom. In particular, do students who sit in the front row get better grades, on average, than the general population of students?

C. Cell phones are everywhere, and we are now available by phone almost all of the time. Does this translate into a change in the closeness of our long-distance relationships?

7.40 Null hypotheses and research hypotheses: For each of the following examples (the same as those in Exercise 7.39), state the null hypothesis and the research hypothesis, in both words and symbolic notation:

a. A researcher is interested in studying the relation between the use of antibacterial products and the dryness of people skin. He thinks these products might alter the moisture in skin compared to other products that are not antibacterial.

b. A student wonders if grades in a class are in any way related to where a student sits in the classroom. In particular, do students who sit in the front row get better grades, on average, than the general population of students?

2. Fill in the blank with the best word or words.

a. Values of a test statistic beyond which you reject the null hypothesis are called ___

b. The _____ ______ is the area in the tails in which the null can be rejected.

c. If your data differ from what you would expect if chance were the only thing operating, you would call your finding ___

d. A hypothesis test in which the research hypothesis is directional is a(n) __ 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.

e. If your z-statistic exceeds the critical cutoff, you can ____ _________ the null hypothesis.

3. The police department of a major city has found that the average height of their 1,250 officers is 71 inches (???????in.) with ? = 2.3 inches.

a. How many officers are at least 75 inches tall?

b. How many officers are between 65 and 72 inches tall?

c. If an officer is at the 35^th percentile in terms of height, how tall is he/she?

d. The top 10% of the officers in terms of height also make higher salaries than the shorter officers. How tall does an officer have to be to get in that top 10% group?

4. The verbal part of the Graduate Record Exam (GRE) has a ? of 500 and ? = 100. Use the normal distribution to answer the following questions:

a. If you wanted to select only students at or above the 90^th percentile, what verbal GRE score would you use as a cutoff score?

b. What verbal GRE score corresponds to a percentile rank of 15%? What verbal GRE score corresponds to a percentile rank of 55%?

c. What’s the percentile rank of a GRE score of 628? What’s the percentile rank of a GRE score of 350?

d. If you randomly selected 1,500 students who had taken the verbal GRE, how many would you expect to score lower than 250? How many would you expect to score higher than 750?

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Part II: SPSS Analysis

1. For this problem, you will be using last module/week’s data set containing IQ scores. Open the file; it will also contain the standardized IQ variable you created last module/week.

a. Using the z-scored IQ variable, create percentile ranks assuming the scores are normally distributed. Call the new percentile variable “IQ rank.”

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

c. 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:There is no Part III material this module/week.

Part IV: Cumulative

1. (Non-SPSS) For a distribution with M = 25 and s = 4:

a. What is the z-score corresponding to a raw score of 20?

b. What is the z-score corresponding to a raw score of 36?

c. If a person has a z-score of 1.2, what is his/her raw score?

d. If a person has a z-score of -.73, what is his/her raw score?

2. (Non-SPSS) 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.

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

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

c. One scale IV and one scale DV.

d. Nominal/categorical variable and percentages.

3. For the following scores, state the: a) mean; b) median; c) mode; d) range; e) standard deviation

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