3. a through 3d are based on a distribution of scores with and the standard devi
ID: 3125396 • Letter: 3
Question
3. a through 3d are based on a distribution of scores with 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?
b. What is the probability of a score falling above a raw score of 80?
c. What is the probability of a score falling between a raw score of 81 and 83?
d. What is the probability of a score falling below a raw score of 63?
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?
he data sets for problems 5 and 6 can be found through the Pearson Materials in the Student Textbook Resource Access link, listed under Academic Resources. The data is listed in the data file named Lesson 20 Exercise File 1. Answer Exercises 5 and 6 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).
5. 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
b. Mode for marital status
c. Frequency of divorced people in the sample
6. Using IBM® SPSS® software, create a frequency table to summarize the data on the educational level variable. Copy and paste the output from IBM® SPSS® into this worksheet.
7. The data set for this problem can be found through the Pearson Materials in the Student Textbook Resource Access link, listed under Academic Resources. The data is listed in the data file named Lesson 21 Exercise File 1. 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
b. Mean
c. Standard deviation
d. Kurtosis
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?
How does understanding probability help you understand statistics?
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?
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?
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?
How does understanding probability help you understand statistics?
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?
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?
Explanation / Answer
Multiple questions. First 2 questions answered.
3. a through 3d are based on a distribution of scores with and the standard deviation = 6.38. Draw a small picture to help you see what is required.
Z value for 70, z=(70-75)/6.38 = -0.78
Z value for 80, z=(80-75)/6.38 = 0.78
P( 70<x<80) = P( -0.78<z<0.78)
=P( z <0.78) – P( z <-0.78)
= 0.7823 - 0.2177 = 0.5646
P( x >80) = P( z >0.78) =0.2177
Z value for 81, z=(81-75)/6.38 = 0.94
Z value for 83, z=(83-75)/6.38 = 1.25
P( 81<x<83) = P( 0.94<z<1.25)
=P( z <1.25) – P( z <0.94)
= 0.8944 - 0.8264 = 0.068
d. What is the probability of a score falling below a raw score of 63?
Z value for 63, z=(63-75)/6.38 = -1.88
P( x <63) =P( z < -1.88)
= 0.0301
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?
Z value for top 10% =1.282
Raw score =mean+z*sd = 78+1.282*5.5 = 85.051
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