Complete Parts A, B, and C below.

Part A

Some questions in Part A require that you access data from Statistics for People Who (Think They) Hate Statistics. This data is available on the student website under the Student Text Resources link.

1. Why is a z score a standard score? Why can standard scores be used to compare scores from different distributions?

A z score is considered a standard score because it is based on the degree of variability within its distribution. Standard scores across different distributions measure in the same fashion. A z score is the result of dividing the amount that a raw score differs from the mean of the distribution by the standard deviation. So, scores below the mean will have negative z scores, and scores above the mean will have positive z scores. Positive z scores always fall to the right of the mean, and negative always fall to the left (Salkind, 2011).

2. For the following set of scores, fill in the cells. The mean is 70 and the standard deviation is 8.

Raw score

Z score

68.0

-0.25

57.2

–1.6

82.0

1.5

84.4

1.8

69.0

–0.125

66.0

–0.5

85.0

1.875

83.6

1.7

72.0

.25

3. Questions 3a through 3d are based on a distribution of scores with image2.png and the standard deviation = 6.38. Draw a small picture to help you see what is required.

a. What is the probability of a score falling between a raw score of 70 and 80? 0.5668

b. What is the probability of a score falling above a raw score of 80? 0.2166

c. What is the probability of a score falling between a raw score of 81 and 83? 0.0686

d. What is the probability of a score falling below a raw score of 63? 0.0300

4. Jake needs to score in the top 10% in order to earn a physical fitness certificate. The class mean is 78 and the standard deviation is 5.5. What raw score does he need? (x-78) / 5.5 = .9 Minimum required score of 85.04

5. Who is the better student, relative to his or her classmates? Use the following table for information.

Math

Class mean

81

Class standard deviation

2

Reading

Class mean

87

Class standard deviation

10

Raw scores

Math score

Reading score

Average

Noah

85

88

86.5

Talya

87

81

84

Z-scores

Math score

Reading score

Average

Noah

2

0.1

1.05

Talya

3

-0.6

1.2

Talya is the better student.

From Salkind (2011). Copyright © 2012 SAGE. All Rights Reserved. Adapted with permission.

Part B

Some questions in Part B require that you access data from Using SPSS for Windows and Macintosh. This data is available on the student website under the Student Text Resources link.

The data for Exercises 6 and 7 are in the data file named Lesson 20 Exercise File 1. Answer Exercises 6 and 7 based on the following research problem:

Ann wants to describe the demographic characteristics of a sample of 25 individuals who completed a large-scale survey. She has demographic data on the participants’ gender (two categories), educational level (four categories), marital status (three categories), and community population size (eight categories).

6. Using IBM® SPSS® software, conduct a frequency analysis on the gender and marital status variables. From the output, identify the following:

a. Percent of men= 52%

b. Mode for marital status= 1

c. Frequency of divorced people in the sample= 11

7. Using IBM® SPSS® software, create a frequency table to summarize the data on the educational level variable.

Descriptive Statistics

N

Minimum

Maximum

Mean

Std. Deviation

Education Level

25

1

4

2.64

1.150

Valid N (listwise)

25

The data for Exercise 8 is available in the data file named Lesson 21 Exercise File 1.

8. David collects anxiety scores from 15 college students who visit the university health center during finals week. Compute descriptive statistics on the anxiety scores. From the output, identify the following:

a. Skewness=.416

b. Mean=32.27

c. Standard deviation=23.478

d. Kurtosis= -1.124 Standard error of Kurtosis = 1.121

From Green & Salkind (2011). Copyright © 2012 Pearson Education. All Rights Reserved. Adapted with permission.

Part C

Complete the questions below. Be specific and provide examples when relevant.

Cite any sources consistent with APA guidelines.

Question

Answer

What is the relationship between reliability and validity? How can a test be reliable but not valid? Can a test be valid but not reliable? Why or why not?

Reliability consists of test re-rest, parallel forms, internal consistency and interrater reliability (Salkind, 2011). For something to be reliable it must remain consistent. This goes for the measurements of the test results. For something to be considered reliable, the same conclusion must be met every time the formula is processed.

Validity contains construct validity, internal validity, external validity and conclusion validity (Salkind, 2011). For something to be valid, it must remain true. So yes, something can be valid but the result may not appear every time exacts are performed so that would not make the formula valid but if something is valid, it performs as expected every time, which makes it reliable Salkind, 2011).

Statistics and probability are related. Probability is based off of statistics past events and looking at the outcomes of the probability of an action or decision reward being favorable to the action determines the probability of the individual’s decision. For example: Gambling at the casino. If someone knows of an individual who does well at the casino, the probability of that individual trying their luck is higher than an individual who does not know anyone or who has not won anything before.

How could you use standard scores and the standard distribution to compare the reading scores of two students receiving special reading resource help and one student in a standard classroom who does not get special help?

Comparing the standard scores and standard distribution from the two students receiving special resource help to the same scores from the individual who is not receiving special help can identify if the extra help is beneficial to two students receiving the help or not compared to the individual who is not receiving the extra help. That is confusing. When testing all three individuals with the same tools, one can identify where everyone is with the reading scores to find if the extra resources are beneficial or not.

In a standard normal distribution: What does a z score of 1 represent? What percent of cases fall between the mean and one standard deviation above the mean? What percent fall between the mean and –1 to +1 standard deviations from the mean? What percent of scores will fall between –3 and +3 standard deviations under the normal curve?

The empirical states that the bulk of data cluster around the mean in a normal distribution.

1. 68% of values fall within +- 1 standard deviation of the mean

2. 95% fall within +- 2 standard deviation of the mean

3. 99% fall with +- 3 standard deviations of the mean (Aron, Aron, & Coups, 2009).