Practice Exercise #7: Hypothesis

1. What is a hypothesis?
2. What is the difference between a population and a sample?
3. Why do researchers use samples?
4. Why is it important for the sample to accurately represent the population?
5. What is the difference between a null hypothesis and a research hypothesis?
6. What are two types of research hypotheses?
7. What is the difference between a directional and non-directional hypothesis?
8. What type of hypothesis corresponds to a one-tail test?

Practice Exercise #8: z-scores

1. What are the three characteristics of the normal curve or normal distribution?
2. What percent of scores fall between -1SD and +1SD on a normal curve?
3. What are standard scores?
4. What is the unit of measurement for standard scores?
5. How would you explain a z score of 1.25 with respect to it position relative to the mean?

Practice Exercise #9: z-scores

Using the following data and the Descriptives function in SPSS to answer each of the following questions:

21 25 21 19 16 18 19 19 16 24 21 21 17 26 20 23 20 21 20

1. What is the mean?
2. What is the standard deviation?
3. What is the z score for each of the following:

1. 16 b. 21 c. 25

4. Assuming the above data was normally distributed, what percent of scores are equal to or less than each of the following scores (Use Table B.1):

1. 20 b. 26 c. 17

5. For a one-tailed test or directional hypothesis, the researcher is interested in results that occur in only one tail of the normal curve (e.g., they are interested in extreme high scores or extreme low scores). Therefore, when using the 5% criteria to judge the likelihood of a score, the researcher identifies the score that divides the curve into two parts (one part containing 95% of the scores and the other part containing 5% of the scores). What value of z separates the normal curve into these two sections? (You may need to refer to Table B.1).

6. For each of the following scores, use the one-tail five percent (5%) criteria and determine if the occurrence of the score would be considered relatively likely or unlikely?

1. 18 b. 24 c. 25

7. For a two-tailed test or nondirectional hypothesis, the researcher is interested in results that occur in either tail of the normal curve (e.g., they are interested in extreme high scores and extreme low scores). Therefore, when using the 5% criteria to judge the likelihood of a score, the researcher identifies the score that divides the curve into three parts (the first part containing the lower 2.5% of scores, the second part containing the middle 95% of the scores, and the third part containing the upper 2.5% of the scores). What value of z separates the normal curve into these three sections? (You may need to refer to Table B.1).

8. For each of the following scores, use the two-tail five percent (5%) criteria and determine if the occurrence of the score would be considered relatively likely or unlikely?

1. 25 b. 26

9. Why was a score of 25 considered unlikely in #6 but not unlikely in #8?

Assignment #2: z-scores

Directions: Use the data from Assignment 1 to answer each of the following questions.

**For this assignment, all answers MUST be rounded to two decimal places. **

1. What is the mean percent of students receiving free or reduced lunch for this district?
2. What is the value of the standard deviation?
3. What is the z score for each of the following percents:
   1. 8
   2. 53
   3. 74
4. Assuming the data was normally distributed, what percent of scores are equal to or less than each of the following scores (Use Table B.1 and round z scores to two decimal places):
   1. 8
   2. 53
   3. 74
5. For each of the following values, use the one-tail five percent (5%) criteria and determine if the occurrence of the score would be considered relatively likely or unlikely? (Note: Assume that the researcher is only interested in the extreme low percents of students receiving free or reduced lunch--or the negative end of the normal curve).
   1. 8
   2. 15
   3. 58
6. For each of the following scores, use the two-tail five percent (5%) criteria and determine if the occurrence of the score would be considered relatively likely or unlikely?
   1. 5
   2. 96

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