Overview
NO AI AT ALL
EVERYTHING YOU NEED WILL BE LINKED BELOW. INSTRUCTIONS: (I will also put a screenshot of them down below.)
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 spread 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
Please make sure to read each problem or exercise carefully and provide ALL your calculations to show me that you are understanding this material (please do not just provide answers without the evidence for how you obtained your answers).
Part A Task: For Part A of Lab #2, you will be using the Lab Assessment #2 Excel data file Download Lab Assessment #2 Excel data fileand 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).
- You will be working with data from two semesters (Winter 2024 and Winter 2025) of Stat 101 students' responses for Anxiety Levels and/or Sleep Hours. The raw scores and z-scores for each variable and both semesters are presented in the Lab Assessment #2 Excel data file. Open the Lab Assessment #2 Excel data file and look over the raw scores and z-scores for each variable and semester. Also, look over the means, medians, modes, and standard deviations for each variable and semester. When asked to briefly explain your answers, please make sure to provide concise and short answers (no more than 1 or 2 sentences).
- Choose ONE variable to work with (Anxiety Levels or Sleep Hours). You must use different variables than the ones you chose in Lab #1 Parts C, D, & E. Look over the raw scores, z-scores, mean, median, and standard deviation for the ONE variable you have chosen. Briefly describe each semester -Winter 2024 & Winter 2025- for the one variable you chose. Remember that there are always 3 things we need to describe: shape (if appropriate), typical value, and spread. Also, remember to use the most appropriate measure of central tendency (typical value) and measure of variability (spread) to describe each section. Which semester is more consistent? Briefly explain your answer. Briefly explain your answer, in one sentence, using only the information in the Lab #2 Excel data file.
- Other factors being equal and using the same variable you chose for 1A, which semester would you predict to have the higher average score? Briefly explain your answer, in one sentence, using only the information in the Lab #2 Excel data file.
- Using the same variable you chose for 1A, are there scores that are more than 2 standard deviations away from the mean? If yes, which specific score(s), which semester(s), and identify if the scores are above or below the mean?
- Using the Winter 2024 and Winter 2025 data for Homework Hours, please answer the following questions.
- Students, in both Winter 2024 and Winter 2025 Stat 101 courses, were asked how much time they spend studying per night. Take a look at the z-scores for both semesters. Which semester did students report more time spent studying relative to their fellow classmates? Briefly explain your answer, in one sentence, using only the information in the Lab #2 Excel data file. (This question does not require looking up probabilities in the Unit Normal Table or z-table.)
- What is the probability that a student from Winter 2024 spent more than 4 hours studying per night? Is this unusual? Why or why not? There are no calculations needed for this question. All z-scores are provided for you in the Lab #2 Excel data file. Please make sure to look up probabilities in the Unit Normal Table (z-table) in Chapters 6, 7, & 8 Modules.
- What is the probability that a student from Winter 2025 spent more than 5 hours studying per night? Is this unusual? Why or why not? There are no calculations needed for this question. All z-scores are provided for you in the Lab #2 Excel data file. Please make sure to look up probabilities in the Unit Normal Table (z-table) in Chapters 6, 7, & 8 Modules.
- What is the probability that a student from Winter 2024 spent less than 2 hours studying per night? Is this unusual? Why or why not? There are no calculations needed for this question. All z-scores are provided for you in the Lab #2 Excel data file. Please make sure to look up probabilities in the Unit Normal Table (z-table) in Chapters 6, 7, & 8 Modules.
- What is the probability that a student from Winter 2025 spent less than 1 hour studying per night? Is this unusual? Why or why not? There are no calculations needed for this question. All z-scores are provided for you in the Lab #2 Excel data file. Please make sure to look up probabilities in the Unit Normal Table (z-table) in Chapters 6, 7, & 8 Modules.
- In a study on academic performance, researchers measure students' test anxiety levels on a scale. The scores are normally distributed with a population mean of 𝜇 = 70 and population standard deviation of 𝜎 = 10. If we transform this distribution into z-scores, then the distribution of z-scores will have a mean of ________ and a standard deviation of ________.
- The cholesterol levels of patients in two hospitals are normally distributed. Hospital A has a mean cholesterol level of 𝜇 = 200 mg/dL with a standard deviation of 𝜎 = 25 mg/dL, while Hospital B has a mean cholesterol level of μ = 190 mg/dL with a standard deviation of 𝜎 =20 mg/dL A patient in Hospital A has a cholesterol level of 225 mg/dL, and a patient in Hospital B has a cholesterol level of 210 mg/dL. Based on their z-scores, which patient has a cholesterol level that is higher relative to their hospital's distribution?
Part B Task: For Part B of Lab #2, you will be identifying probability models and calculating probabilities.
5. The tables below provide probabilities for bags of M & Ms. For each of the tables below, you will need to identify and state whether the tables are probability models or not and explain why or why not
5A. Is the table below a probability model? Why or why not? Briefly explain using probability rules.
| M & M Color | Probability |
|---|---|
| Brown | .30 |
| Yellow | .20 |
| Red | .20 |
| Blue | .10 |
| Orange | .15 |
| Green | .10 |
5B. Is the table below a probability model? Why or why not? Briefly explain using probability rules.
| M & M Color | Probability |
|---|---|
| Brown | .25 |
| Yellow | .20 |
| Red | -.25 |
| Blue | .15 |
| Orange | .10 |
| Green | .05 |
5C. Is the table below a probability model? Why or why not? Briefly explain using probability rules.
| M & M Color | Probability |
|---|---|
| Brown | .25 |
| Yellow | .20 |
| Red | .15 |
| Blue | 1.05 |
| Orange | .10 |
| Green | .15 |
5D. Is the table below a probability model? Why or why not? Briefly explain using probability rules. Also, what does this table of probabilities imply?
| M & M Color | Probability |
|---|---|
| Brown | 0 |
| Yellow | .50 |
| Red | 0 |
| Blue | .25 |
| Orange | 0 |
| Green | .25 |
- The following table provide probabilities for bags of Skittles. Please use this table to answer the following 4 questions (6A, 6B, 6C, & 6D).
| Skittles Color | Probability |
|---|---|
| Red | .20 |
| Yellow | .25 |
| Green | .15 |
| Orange | .25 |
| Purple | .15 |
- Is this a probability model? Why or why not? Explain using probability rules.
- If an individual buys a bag of skittles, picks one skittle at a time out of the bag randomly, and replaces the skittle after each pick, what is the probability that the individual picks a red, yellow, or purple skittle? Please make sure to show your calculations. Interpret this probability, in one sentence.
- If an individual buys a bag of skittles, picks one skittle at a time out of the bag randomly, and replaces the skittle after each pick, what is the probability that the individual picks two skittles (with replacement) that are green and orange? Please make sure to show your calculations. Interpret this probability, in one sentence.
- If an individual buys a bag of skittles, picks one skittle at a time out of the bag randomly, and replaces the skittle after each pick, what is the probability that the individual does not pick a red skittle? Please make sure to show your calculations. Interpret this probability, in one sentence.
- 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.
- Roughly __________ of the total area under the normal curve is within one standard deviation of the mean.
Part C Task: For Part C of Lab #2, you will be using the Unit Normal Table (to look up z-scores and probabilities and to look up probabilities to determine z-scores), which you will find in Chapter 8 Module under Learning Activities.
- A population of statistics students reported how many hours they slept last night. This distribution is normally distributed with a mean of 6.96 (µ = 6.96) and a standard deviation of 1.82 (σ = 1.82).
- What percent of statistics students sleep more than 8 hours? Is this unusual? Please briefly explain why or why not, in one sentence.
- What is the lowest number of sleep hours that would place students in the top 10% of this distribution?
- A random sample of 25 students is drawn from this population. What is the probability that the mean sleep hours is greater than 8 hours? Is this unusual? Please briefly explain why or why not, in one sentence.
Part D Task: For Part D of Lab #2, you will be conducting a hypothesis test and using the Unit Normal table (to look up z-scores and probabilities), which you will find in Chapter 8 Module under Learning Activities.
10. A psychologist is interested in whether the average number of hours per week that individuals spend on social media is more than 10 hours (μ = 10), with a population standard deviation of 3 hours (σ = 3 hours). A random sample of 64 individuals (n = 64) has an average social media usage of 11 hours (M = 11 hours). Does this sample provide enough evidence to conclude that individuals spend more hours on social media than the general population?
State the null and research (alternative) hypotheses in words and using symbols. Conduct the appropriate hypothesis test with a = .05 and state your conclusion in terms of this problem. Make sure to write conclusions in APA format as shown in lecture/example videos. Don't forget to include effect size, if applicable and confidence interval.
11. A study investigated the average number of hours spent exercising per week among adults.
The researchers found that the average number of hours spent exercising per week among 150 adults (M = 3.5 hours) was significantly greater than the national average, z(n = 150) = 2.89, p < .01, d = .49, medium effect, 95% CI [3.25, 3.75].
Based on the statement above, please answer the following:
- What is sample size? What is the specific statistical evidence that helped you answer this question?
- What is the direction of the difference between sample mean and population mean? What is the specific statistical evidence that helped you answer this question?
- What is the decision (fail to reject or reject the null hypothesis? What is the specific statistical evidence that helped you answer this question?
- What is effect size in this study? What is the specific statistical evidence that helped you answer this question?
- What is the interpretation for this effect size? How likely is it that we will get the same results if we replicate this hypothesis test with different samples?