WEB CALCULATOR EXERCISE
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?
Mean Age- 47.5, calculated by adding all numbers together and deviding by 20
Standard dev-10.7483, step 1 Calculated by taking each persons main age subtracting mean age squaring result, step 2 take sum of squares, step 3 found N=total number of values-1 which was 20-1 N-1=19, step 4 divide square root of step 2 by square root of step 3
b. Create a frequency distribution table for denomination.
Denomination Frequency How calculated
Counted how many people were in each church.
Put frequency for each denomination.
Episcopal 1
Lutheran 2
Methodist 0
Presbyterian 2
Other Main Line Protestant 1
Baptist 3
Other Evangelical Protestant 3
Pentacostal 1
Charismatic 3
Non-Denominational 3
Catholic 0
Other 1
c. What is the percentage of people who identify themselves as Baptist in this sample?
15%, 3 of 20 defined themselves as Baptist so 3 divided by 20 is.15 times 100 is 15%
d. What is the mode of church attendance?
The mode of church attendance is 5, or twice a week
Step 1 order numbers in numerical order, step 2 find which number occurs most often, most occurances is 5
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?
Z score is 2.8571, step one subtract mean from value, step 2 divide difference by standard deviation. Step 3 look of quotient in z table
b. What is a Z score for a car with a price of $30,000?
Z score is 2.0000, step one subtract mean from value, step 2 divide difference by standard deviation. Step 3 look of quotient in z table
c. At what percentile rank is a car that sold for $30,000?
97.72 % find z score and use z score to percentile calculator to figure out percentile
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?
English exam. Step one-find standard deviation, step 2 find percentile, step 3 compare percentile.
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?
Z score is 0, X=Andrews score=45 mean-45 sd-4
X-mean\sd=0
b. If Anna scored 30 on this test, what is her Z score?
Z=-3.75, X=annas score= 30 mean-45 sd-4
X-mean/sd= -3.75
c. If Bill’s Z score was 1.5, what is his real score on this test?
1.5=x-45/4 (1.5)4=(x-45\4)4 6=x-45 6+45=x x=51
d. There are 200 students in a sample. How many of these students will have scores that fall under the score of 41? Z=41-45/4 Z=41-45=-4/4=-1
Z=-1
According to Jackson Z=-1=.159
.159*200(people in survey)=31.8
Or Approximately 32
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
Pearson R-.59 Coefficiant of determination- .35
b. Between the IQ and statistics scores
Pearson R- .74 Coefficiant of determination- .55
c. Between the psychology scores and statistics scores.
Pearson R.- .71 Coefficiant of determination- .5
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
Correlation coefficient- .8519
Rounded to approximately.85
ARE MY ANSWERS RIGHT???
PLEASE ADVISE
Based on the information provided, here are the correct answers:
1. The mean age of the sample is 47.5 and the standard deviation is 10.7483.
2.
a. The Z-score for a car with a price of $33,000 is 2.8571.
b. The Z-score for a car with a price of $30,000 is 2.0000.
c. The car that sold for $30,000 is at approximately the 97.72th percentile.
3. The student did better in the English exam.
4.
a. Andrew's Z-score is 0.
b. Anna's Z-score is -3.75.
c. Bill's real score on the test is 51.
d. Approximately 32 students will score below 41.
5.
a. The Pearson's r for the relationship between IQ and psychology scores is -0.59 and the coefficient of determination is 0.35.
b. The Pearson's r for the relationship between IQ and statistics scores is 0.74 and the coefficient of determination is 0.55.
c. The Pearson's r for the relationship between psychology scores and statistics scores is -0.71 and the coefficient of determination is 0.5.
6. The correlation coefficient for the relationship between the number of cups of coffee and stress level is approximately 0.85.
These answers are correct based on the information provided.
Your answers are mostly correct. However, there are a few errors in your calculations:
1. The mean age of the sample is calculated correctly as 47.5, but the calculated standard deviation is incorrect. The correct standard deviation is approximately 11.17, not 10.7483.
2. The percentage of people who identify as Baptist is not 15%, but rather 15/20 = 0.75, which is 75%. So the correct answer is 75%.
3. The mode of church attendance is not 5, but rather 2 or once a month. It is the value that occurs most frequently in the dataset.
4. For the first problem, the Z-score for a car priced at $33,000 is approximately 2.29, not 2.8571. For a car priced at $30,000, the Z-score is approximately 1.43, not 2.0000.
5. For the second problem, the correct answer is English exam. Since the score of 84 is above the mean of 78, it indicates a better performance in English compared to the score of 70 in math.
6. For the fourth problem, all your answers are correct. Andrew's Z-score is indeed 0, Anna's Z-score is -3.75, and Bill's real score would be 51.
7. For the fifth problem, all your answers are correct. The Pearson's r values and coefficients of determination for the three relationships are correctly calculated.
8. For the sixth problem, the correlation coefficient is correctly calculated as approximately 0.852 or 85.2%.
Overall, you did a good job, but please double-check the calculations and pay attention to any potential errors.