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Revision Due Date:Monday, 12/5 at 8 pm
This lab assessment closes on Monday, 12/5 at 8 pm. This means you will no longer have access to the lab after 8 pm on Monday, 12/5.
Purpose: Remember that descriptive statistics are used to describe the variables in a study. Our last Assessment focused on descriptive statistics, primarily describing shape, typical values, and variability of a data set. Remember that there are 3 things we always want to know about our data: shape, center, and spread. In Chapter 5, we explored how to transform raw data into a standard normal distribution so that we can compare different distributions of data. In Chapter 6, we explored probability, which is essential for inferential statistics.In Chapter 7, we explored sampling distributions and in Chapter 8, we explored a statistical procedure (z-tests) to test hypotheses about population data.This learning activity will assess your ability to: (a) transform a set of data into the standard normal distribution of z-scores and interpret these z-scores, (b) determine appropriateness of probability models, (c) calculate and interpret probabilities, (d)calculate probabilities for population and sampling distribution, (e) conduct hypothesis tests, and (f) write APA style conclusions. Variability and probability are at the core of statistics. We will be revisiting these concepts throughout the rest of our course.
Skills:The purpose of this assessment is to help you practice the following skills that are essential to your success in this course and in your professional life beyond school:
transforming data into z-scores and interpreting these z-scores
evaluating appropriateness of probability models
calculating and interpreting probabilities
- calculating probabilities for population and sampling distributions
- using hypothesis tests to draw conclusions about the population using sample data
- calculating confidence intervals
- calculating effect size, when applicable
- interpreting and communicating statistical results
Knowledge:This assessment will also help you to become familiar with the following important content knowledge in elementary statistics:
transforming raw data into z-score to determine probabilities
evaluating appropriateness of probability models
calculating and interpreting probabilities
- calculating z-scores and finding the corresponding probabilities
- conducting hypothesis tests
- reporting statistical findings in APA format
Part A Task:For this part of Lab #2, we will be using the Assessment 3 Data Excel file and the Unit Normal Table to look up z-scores and probabilities, which you will find in Chapter 8 Module under Learning Activities. You will need access to a computer with Microsoft Excel and Word. Remember that everyone has access to Office 365 (which includes Microsoft Excel and Word) in our Canvas course in the left navigation. If you choose to use Google Docs, please make sure to download your file into a Word document (.docx).
Two sections in History classes were given an academic aptitude test. The raw scores and z-scores for each group are presented in the Assessment 3 Data Excel file. Open the Assessment 3 Excel file and look over the raw scores and z-scores for each section in the History Scores tab. Also, look over the means and standard deviations for each section.
Briefly describe each section (shape, typical value, and spread). Remember to use the most appropriate measures of central tendency (typical value) and measure of variability (spread) to describe each section. Which group is more consistent with respect to academic aptitude as measured by the test? Briefly explain your answer.
Other factors being equal, which group would you predict to have the higher average score on the final exam in the course? Briefly explain your answer.
In Sections 1 & 2, are there scores that are more than 2 standard deviations above the mean or 2 standard deviations below the mean? If yes, which score(s) and which section(s)?
The scores for 15 persons on the Stressful Life Events Inventory (SLEI) and the scores for 15 other persons on the Major Stressors Questionnaire (MSQ) are presented in the Assessment 3 Data Excel file in the Stress Scores tab. For both surveys, higher scores mean that the person has experienced more stressors recently, suggesting a greater risk for stress-related symptoms such as acute anxiety attacks. Open the Assessment 3 Data Excel file and look over the SLEI and MSQ raw scores and z-scores in the Stress Scores tab.
Please take a look at Participant 8 and 23 raw scores and z-scores. Who is at the greatest risk for acute anxiety attacks, Participant 8 or 23? Please make sure to briefly explain your answer based on the z-scores.
What is the probability that someone will score higher than 40 on the SLEI? Is this unusual? Why or why not? What is the probability that someone will score higher than 125 on the MSQ? Is this unusual? Why or why not? (Please make sure to look up probabilities in the Unit Normal Table in Appendix B)
What is the probability that someone will score lower than a 21 on the SLEI? Is this unusual? Why or why not? What is the probability that someone will score lower than a 110 on the MSQ? Is this unusual? Why or why not? (Please make sure to look up probabilities in the Unit Normal Table in Appendix B)
3.A company hired a psychologist to assist their employees in their personal problems. The psychologist kept 1 file for each person they helped. Eight (8) employees sought out help for drug-related problems. Fifteen (15) employee needed help for family crisis problems. And twenty-two (22) employees needed help for miscellaneous reasons. The numbers are summarized below.
If one of the files is selected at random, what is the probability that it would involve a drug-related case? Interpret this probability.
If one of the files is selected at random, what is the probability that it would involve a miscellaneous case? Interpret this probability.
If one of the files is selected at random, what is the probability that it would involve a drug-related case or a family crisis case? Interpret this probability.
Please fill in the blanks for each of the following sentences.
4. If an entire population IQ scores withµ= 500 andσ= 25 is transformed into z-scores, then the distribution of z-scores will have a mean of ________ and a standard deviation of ________.
5. One of the central ideas about probability is that chance behavior has an unpredictable pattern in the __________ run, a regular and predictable pattern in the __________ run.
6. Roughly __________ of the total area under the normal curve is within one standard deviation of the mean.
Part B Task:
For this part of Lab #2, we will be using the Unit Normal Table to look up z-scores and probabilities, which you will find in Chapter 8 Module under Learning Activities.
7. A population of statistics students reported the typical number of hours that they sleep, on average, every night. This distribution is normally distributed with a mean ofµ= 6.7 hours and a standard deviation ofσ= 1.02 hours.
- What
percent
of statistics students sleep more than 7 hours? Is this unusual? Please briefly explain why or why not.
- What is the lowest number of sleep hours that would place students in the top 15% of this distribution?
- A random sample of 16 students is drawn from this population. What is the probability that the mean hours of sleep is greater than 7 hours? Is this unusual? Please briefly explain why or why not.
8. In a 2003 study of the long-term effects of concussions in football players, researchers concluded that college football players receive a meanofµ= 50 strong blows to the head, each with an average of 40G (40 times the force of gravity). Assume this distribution is approximately normal with a standard deviation of
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= 16 on a risk-taking questionnaire. A different group of researchers believe that football players receive less strong blows to the head. They obtained a sample of n = 49 college football players and the sample data produced a sample mean ofM= 45. Does this sample of college football players provide enough evidence to conclude that they receive less strong blows to the head than the general population college football players?
State the null and research (alternative) hypotheses in words and using symbols. Conduct the appropriate hypothesis test witha= .05 and state your conclusion in terms of this problem. Make sure to write conclusions in APA format as shown in lecture videos. Don't forget to include effect size, if applicable and confidence interval.
Please fill in the blanks for each of the following sentences.
9. Suppose that a professor randomly assigns students to study groups of n = 25 students. The final exam in the professor's class has a mean ofµ= 76 andσ= 4. This distribution of study group means will have an expected mean value of __________ and a standard error of __________.
10. The boundaries for the critical region are determined by ______________.
11. If a hypothesis test is found to have power = 0.85, then the probability of a Type II error for that same test is __________.
12. For each of the following examples, identify whether the research has expressed a directional of non-directional hypothesis:
A. A researcher is interested in studying the use of antibacterial products and the dryness of people's skin. They think these products might reduce the moisture in skin compared to other products that are not antibacterial.
B. A student wonders if grades in a class are in any way related to where a student sits in the classroom. In particular, do students who sit in the front row get better grades, on average, than the general population of students?
C. Cell phones are everywhere and we are now available by phone almost all of the time. Does this affect closeness of long-distance relationships?
Criteria for Success:
Interpretation of z-scores and corresponding probabilities are provided
Probability models are evaluated for appropriateness and explanations are provided
Probabilities are calculated and interpreted accurately
Analysis and interpretations are reported in such a way that someone with no statistical background would understand
- Null and alternative hypotheses are correctly stated
- Includes hypotheses both in symbols and words
- Interpretation of z-scores and corresponding probabilities are provided
- Data are correctly analyzed and interpreted
- Correct statistical procedures are used
- Confidence intervals are calculated
- Effect size is calculated, when applicable
- Statistical conclusions are correctly reported and are APA format