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

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?

4a. To find Andrew's Z score, we first need to calculate the standard score using the formula:

Z = (X - μ) / σ

Where:
X = Andrew's score on the test = 45
μ = Mean of the distribution = 45
σ = Standard deviation of the distribution = 4

Plugging in the values, we get:

Z = (45 - 45) / 4
Z = 0 / 4
Z = 0

Therefore, Andrew's Z score is 0.

4b. To find Anna's Z score, we use the same formula:

Z = (X - μ) / σ

Where:
X = Anna's score on the test = 30
μ = Mean of the distribution = 45
σ = Standard deviation of the distribution = 4

Plugging in the values, we get:

Z = (30 - 45) / 4
Z = -15 / 4
Z = -3.75

Therefore, Anna's Z score is -3.75.

4c. To find Bill's real score given his Z score, we rearrange the formula:

X = Z * σ + μ

Where:
Z = Bill's Z score = 1.5
σ = Standard deviation of the distribution = 4
μ = Mean of the distribution = 45

Plugging in the values, we get:

X = 1.5 * 4 + 45
X = 6 + 45
X = 51

Therefore, Bill's real score on this test is 51.

4d. To find the number of students out of 200 that will have scores lower than 41, we need to use the Z distribution table.

First, we find the Z score corresponding to a score of 41:
Z = (41 - 45) / 4
Z = -1

Next, we look up the area in the Z distribution table for a Z score of -1. This gives us the proportion of the distribution that falls below -1.

Assuming the distribution is symmetric (which is often the case with normal distributions), we can find the proportion of scores higher than 41 by subtracting the proportion below -1 from 0.5 (since the total area under the normal distribution curve is 1).

Let's say the proportion below -1 is 0.1587. Then the proportion above -1 is:
0.5 - 0.1587 = 0.3413

To find the number of students out of 200 with scores lower than 41, we multiply the proportion above -1 by the total number of students:
0.3413 * 200 = 68.26

Approximately 68 students out of the 200 will have scores that fall under the score of 41.

5a. To find the Pearson's correlation coefficient and coefficient of determination between IQ and psychology scores, we can use a web calculator that accepts data input. We need to enter the IQ scores and the corresponding psychology scores for each student.

5b. To find the Pearson's correlation coefficient and coefficient of determination between IQ and statistics scores, we can use a web calculator that accepts data input. We need to enter the IQ scores and the corresponding statistics scores for each student.

5c. To find the Pearson's correlation coefficient and coefficient of determination between psychology scores and statistics scores, we can use a web calculator that accepts data input. We need to enter the psychology scores and the corresponding statistics scores for each student.

6. To obtain the correlation coefficient for the relationship between the number of cups of coffee and stress level, we can use a web calculator that accepts data input. We need to enter the values for the number of cups of coffee and the corresponding stress levels for each student. The calculator will provide us with the correlation coefficient.