For a population with a mean of 250 and a standard deviation of 47, return each of the following z scores to raw scores on this variable.
a. 0.54
b. -2.66
c. -1.0
d. 1.79
Z = (score-mean)/SD
I'll let you do the calculations.
Descriptive Statistics
1. The table below presents data for a sample of people who completed a religious survey.
Age Gender Denomination Church Attendance
56 1 7 4
46 2 6 5
49 2 6 5
49 1 1 5
27 2 9 5
51 1 4 2
47 2 2 3
67 1 5 4
49 2 2 6
33 1 12 6
55 2 9 5
40 1 7 5
62 1 8 6
47 2 6 3
56 2 9 5
22 1 10 2
50 2 4 5
51 1 10 6
50 1 7 6
43 1 10 3
In this table, the numbers in the gender, denomination, and church attendance columns represent the following.
Gender
1. Male
2. Female
Denomination
1. Episcopal
2. Lutheran
3. Methodist
4. Presbyterian
5. Other mainline Protestant
6. Baptist
7. Other Evangelical Protestant
8. Pentecostal
9. Charismatic
10. Non-denominational
11. Catholic
12. Other
Church Attendance
1. less than once a month
2. once a month
3. a few times a month
4. once a week
5. twice a week
6. three or more times a week
a. What is the mean age of this sample? What is the standard deviation?
b. Create a frequency distribution table for denomination.
c. What is the percentage of people who identify themselves as Baptist in this sample?
d. What is the mode of church attendance?
2. The results of a recent survey indicate that the average new car costs $23,000, with a standard deviation of $3,500. The price of cars is normally distributed.
a. What is a Z score for a car with a price of $ 33,000?
b. What is a Z score for a car with a price of $30,000?
c. At what percentile rank is a car that sold for $30,000?
3. In one elementary school, 200 students are tested on the subject of Math and English. The table below shows the mean and standard deviation for each subject.
Mean SD
Math 67 9.58
English 78 12.45
One student’s Math score was 70 and the same individual’s English score was 84. On which exam did the student do better?
4. Suppose you administered an anxiety test to a large sample of people and obtained normally distributed scores with a mean of 45 and standard deviation of 4. Do not use web-calculator to answer the following questions. Instead, you need to use the Z distribution table in Appendix A in Jackson’s book.
a. If Andrew scored 45 on this test. What is his Z score?
b. If Anna scored 30 on this test. What is her Z score?
c. If Bill’s Z score was 1.5, what is his real score on this test?
d. There are 200 students in a sample. How many of these students will have scores that fall under the score of 41?
5. The table below shows Psychology exam scores, Statistics Exam scores, and IQ scores for a random sample of students. What can you observe in the relationship between IQ and psychology, psychology and statistics, and IQ and statistics? Using a web-calculator, obtain the Pearson’s r and coefficient of determination for the following relationships.
a. Between the IQ and psychology scores
b. Between the IQ and statistics scores
c. Between the psychology scores and statistics scores.
Student number IQ Psychology Statistics
101 142 49 49
102 100 30 32
103 103 36 38
104 121 44 41
105 120 35 42
106 115 47 43
107 101 37 35
108 109 45 47
109 111 30 43
110 115 49 46
6. In a study on caffeine and stress, college students indicated how many cups of coffee they drink per day and their current stress level on a scale of 1 to 10. The table shows the survey results. Using a web-calculator, obtain the appropriate correlation coefficients.
Number of cups of coffee Stress level
3 5
2 3
4 3
6 9
5 4
1 2
7 10
3 5
To convert a z-score to a raw score, you can use the formula:
Raw score = (z-score * standard deviation) + mean
Now, let's calculate the raw scores for each given z-score:
a. z-score = 0.54
Raw score = (0.54 * 47) + 250
Raw score = 25.38 + 250
Raw score = 275.38
b. z-score = -2.66
Raw score = (-2.66 * 47) + 250
Raw score = -125.02 + 250
Raw score = 124.98
c. z-score = -1.0
Raw score = (-1.0 * 47) + 250
Raw score = -47 + 250
Raw score = 203
d. z-score = 1.79
Raw score = (1.79 * 47) + 250
Raw score = 84.13 + 250
Raw score = 334.13
Therefore, the raw scores for each of the given z-scores are:
a. 275.38
b. 124.98
c. 203
d. 334.13