STAT Data Analysis Assignment 3

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STAT 250 Spring 2019 Data Analysis Assignment 3

Your submitted document should include the following items. Points will be deducted if the following are not included.

  1. Type your Name and STAT 250 with your correct section number (e.g. STAT 250-xxx) right justified and then Data Analysis Assignment #2 centered on the top of page 1 below your name the begin your document.
  2. Number your pages across your entire solutions document.
  3. Your document should include the ANSWERS ONLY with each answer labeled by its corresponding number and subpart. Keep the answers in order. Do not include the questions in your submitted document.
  4. Generate all requested graphs and tables using StatCrunch.
  5. Upload your document onto Blackboard as a Word (docx) file or pdf file using the link provided by your instructor. It is your responsibility for uploading a readable file.

Full assignment Instructions, as well as a example is attached as a word file.

Access to StatCrunch is required.

https://www.statcrunch.com/5.0/group.php?groupid=7...

I will provide the login info...

Extra Notes:

- Each graph title should start with "Distribution of.."

- For the questions that require calculation, you can do it on a paper but would have to type the solution into word document.

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STAT 250 Spring 2019 Data Analysis Assignment 3 Your submitted document should include the following items. Points will be deducted if the following are not included. 1. Type your Name and STAT 250 with your correct section number (e.g. STAT 250-xxx) right justified and then Data Analysis Assignment #3 centered on the top of page 1 below your name the begin your document. 2. Number your pages across your entire solutions document. 3. Your document should include the ANSWERS ONLY with each answer labeled by its corresponding number and subpart. Keep the answers in order. Do not include the questions in your submitted document. 4. Generate all requested graphs and tables using StatCrunch. 5. Upload your document onto Blackboard as a Word (docx) file or pdf file using the link provided by your instructor. It is your responsibility for uploading a readable file. 6. You may not work with other individuals on this assignment. It is an honor code violation if you do. Elements of good technical writing: Use complete and coherent sentences to answer the questions. Graphs must be appropriately titled and should refer to the context of the question. Graphical displays must include labels with units if appropriate for each axis. Units should always be included when referring to numerical values. When making a comparison you must use comparative language, such as “greater than”, “less than”, or “about the same as.” Ensure that all graphs and tables appear on one page and are not split across two pages. Type all mathematical calculations when directed to compute an answer ‘by-hand.’ Pictures of actual handwritten work are not accepted on this assignment. When writing mathematical expressions into your document you may use either an equation editor or common shortcuts such as: x can be written as sqrt(x), p̂ can be written as p-hat, x can be written as x-bar. 1 Problem 1: Confidence Interval for Percentage of A’s. The data set “STAT 250 Final Exam Scores” contains a random sample of 269 STAT 250 students’ final exam scores (maximum of 80) collected over the past two years. Answer the following questions using this data set. a) What proportion of students in our sample earned A’s on the final exam? A letter grade of A is obtained with a score of 72 or higher. Hint: You can do this many ways, but in StatCrunch, go to Data → Row Selection → Interactive Tools. In the slider selectors box, click the variable “Scores” into the variable box. Then click compute. Use the slider to obtain the count by looking at the “# rows selected” presented in the first line of the box. Show your work (i.e. describe the method you used to obtain the number of A’s) and express this value as a proportion rounded to four decimal places. b) Assuming there is a big population of students who have completed the final exam in STAT 250, write one sentence each to check the two other conditions of the Central Limit Theorem. c) Using the sample proportion obtained in (a), construct a 95% confidence interval to estimate the population proportion of students who earned an A on the final exam. Please do this “by hand” using the formula and showing your work (please type your work, no images accepted here). Round your confidence limits to four decimal places. d) Verify your result from part (c) using Stat → Proportions Stats → One Sample → With Summary. Inside the box, enter the number of students who earned an A as the # of successes, the sample size as the # of observations, and select confidence interval and click Compute! Copy and paste your StatCrunch result in your document. e) Interpret the StatCrunch confidence interval in part (d) in one sentence using the context of the question. f) Use the Confidence Interval applet (for a Proportion) in StatCrunch to simulate constructing one thousand 95% confidence intervals assuming the proportion of A’s in the population is p = 0.11 and the sample size n = 269. Once the window is open, click reset and select (or click) 1000 intervals. Copy and paste your image into your document. 2 Box 1: Enter the given population proportion, 0.11 Box 2: Enter the given confidence level 0.95 Box 3: Enter the given sample size, n=269 g) Compare the “Prop. contained” value from part (f) to the confidence level associated with the simulation in one sentence. h) Write a long-run interpretation for your confidence interval method in context in one sentence. Problem 2: Food Delivery Robots As we all know, GMU began a robot food delivery service in January. One of the potential benefits of this service is to help the busiest students eat breakfast. Research has shown that about 88% of college students skip breakfast due to busy schedules and other reasons. Initial data were collected from a random sample of 291 Mason students who utilize the robot food delivery service and are presented in StatCrunch. The responses (0 = ate breakfast and 1 = did not eat breakfast) are found in StatCrunch in a data set called “Food Delivery Robots.” a) Obtain the sample proportion of individuals who said “they did not eat breakfast” using Stat → Tables → Frequency in StatCrunch. Only the value of the sample proportion is needed in your answer. Present this sample proportion as a decimal rounded to 4 decimal places. b) Using  = 0.05, is there sufficient evidence to conclude that less than 88% GMU students who utilize the food delivery robots skip breakfast? Conduct a full hypothesis test by following the steps below. i. ii. iii. iv. Define the population parameter in one sentence. State the null and alternative hypotheses using correct notation. State the significance level for this problem. Check the three conditions of the Central Limit Theorem that allow you to use the one-proportion z-test using one complete sentence for each condition. Show work for the numerical calculation. Assume the population is large. 3 v. Calculate the test statistic “by-hand.” Show the work necessary to obtain the value by typing your work and provide the resulting test statistic. Do not round while doing the calculation. Then, round the test statistic to two decimal places after you complete the calculation. vi. Calculate the p-value using the standard Normal table and provide the answer. Use four decimal places for the p-value. vii. State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence (compare your p-value to the significance level to do this). viii. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences. ix. Use StatCrunch (Stat → Proportion Stats → One Sample → with Data) to verify your test statistic and p-value. Copy and paste this box into your document. Problem 3: GMU Shuttle Service GMU officials are trying to determine if they are using the correct number of campus shuttles for the number of individuals who use them. If the proportion of individuals associated with GMU (including faculty, staff, and students) who use the shuttles is significantly different from 0.28, the officials believe they will have to either remove or add a shuttle to the fleet. In a random sample of 444 people taken from the population of all individuals associated with GMU (including faculty, staff, and students) it was discovered that 123 of these individuals use the shuttle. a) Check the three conditions of the Central Limit Theorem that allow you to use the oneproportion confidence interval using one complete sentence for each condition. Show work for the numerical calculation. b) Construct a 99% confidence interval to estimate the population proportion of these individuals who use the shuttle system. Calculate this “by hand” using the formula and showing your work (please type your work, no images accepted here). Round your confidence limits to four decimals. c) Verify your result in part (b) using Stat → Proportions Stats → One Sample → With Summary. Copy and paste your StatCrunch result in your document as well. d) Using  = 0.01, is there sufficient evidence to conclude that the proportion of the individuals who use GMU shuttles is different from 0.28? Conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document. i. ii. iii. iv. Define the population parameter in one sentence. State the null and alternative hypotheses using correct notation. State the significance level for this problem. Calculate the test statistic “by-hand.” Show the work necessary to obtain the value by typing your work and provide the resulting test statistic. Do not round 4 v. vi. vii. viii. during the calculation. Then, round the test statistic to two decimal places after you complete the calculation. Calculate the p-value using the standard Normal table and provide the answer. Use four decimal places for the p-value. State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence (compare your p-value to the significance level to do this). State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences. Use StatCrunch (Stat → Proportion Stats → One Sample → with Summary) to verify your test statistic and p-value. Copy and paste this box into your document. e) Explain the connection between the confidence interval and the hypothesis test in this problem (discuss this in relation to the decision made from your hypothesis test and connect it to the confidence interval you constructed in part (b)). Answer this question in one to two sentences. Problem 4: Building another Sampling Distribution We will use the Sampling Distribution applet in StatCrunch to investigate properties of sampling distributions of the mean for a right skewed distribution. Under Applets, open the Sampling distribution applet (box shown below). First, select “right skewed” for the population and then click on Compute. a) Once the applet box is opened, enter 5 in the box to the right of the words “sample size” in the right middle of the applet box window. Then, at the top of the applet, click “1 time.” Watch the resulting animation. When the sample is completed, copy and paste the entire applet box (using options → copy) into your document. b) Click Reset at the top of the applet. Then, click the “1000 times” to take 1000 samples of size 5. Copy and paste the applet image into your document. c) Describe the shape of the Sample means graph at the bottom of your image from part (b) in one sentence. d) Why do you think that this graph does not have an approximately Normal shape? Use the Central Limit Theorem large sample size condition (for means) to answer this question in one sentence. e) Click Reset at the top of the applet. Type 40 in the sample size box. Then, click the “1000 times” to take 1000 samples of size 40. Copy and paste the applet image into your document. 5 f) Describe the shape of the Sample means graph at the bottom of your image from part (e) in one sentence. g) Why do you think that this graph from part (f) has the shape you described? Use the Central Limit Theorem large sample size condition (for means) to answer this question in one sentence. h) Using the image in part (e), write the values you obtained for the mean (in green) and the standard deviation (in blue). These values are found in the bottom right box labeled “Sample Means” i) Compare the mean value (in green, found in part (h)) to the known mean of the population from the top box labeled “Population.” j) Now calculate the standard error of the sample mean using the value labeled “Std. dev.” in blue from the top box. Round this value to three decimal places. k) Compare the value in part (j) to the standard deviation (in blue) you obtained in part (h) in one sentence. l) Assuming this right skewed population distribution had a population mean of 14.05 and a standard deviation of 11.83; calculate the probability that, in a random sample of 30, the mean of the sample is greater than 16. First, draw a picture with the mean labeled, shade the area representing the desired probability, standardize, and use the Standard Normal Table (Table 2 in your text) to obtain this probability. Please take a picture of your hand drawn sketch and upload it to your Word document (if you do not have this technology, you may use any other method (i.e. Microsoft paint) to sketch the image). You must type the rest of your “by hand” work to earn full credit. m) Verify your answer in part (l) using the StatCrunch Normal calculator and copy that image into your document. In addition, write one sentence to explain what the probability means in context of the question. 6 1 Sample Solution to Display Formatting Problem X: Students’ Grades A random sample of 30 students was selected from a STAT 250 course taught during the summer session and their first exam scores were recorded. a) Create a histogram in StatCrunch. Be sure to title and label it correctly. b) Interpret the histogram’s shape See sample solution and formatting on page 2. Notes about submission Following the main points will help you submit a professionally completed assignment. 1) 2) 3) 4) Right justify your name and provide your correct section and the due date. Center the specific homework assignment title. Bold each problem complete problem number. The graph can be around the below size for readability (click on the graph once and only adjust the size of the graph by using the bottom right dot) 5) Remember not to include the questions in your answer. Only provide answers. Please keep the assignment in problem and part order (present 1a, then 1b, and so on). 2 Kenneth Strazzeri STAT 250-0xx (your correct section) Data Analysis Assignment 1 Problem X a) b) The shape of this distribution is left skewed because I see the majority of the data values falling in the upper end of the distribution and a few 50s and 60s skewing the shape. There does not seem to be any outliers visible on the graph.
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Name
STAT 250-0xx (your correct section)

Data Analysis Assignment #3
Problem 1: Confidence Interval for Percentage of A’s.
a) The proportion of students in our sample who earned A’s on the final exam is represented
by the number with a score of 72 or higher which is 25. In StatCrunch, this is obtained
from the interactive too...


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