Section 3 Lab Document (1)-1

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Clemson University *

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3090

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Statistics

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Feb 20, 2024

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STAT 3090 S ECTION 3 L AB S PRING 2024 N AME : P URPOSE : It is as important to be able to communicate and explain data distributions as it is to be able to produce graphs and calculate statistics. The following questions will help you become proficient using your calculator and software to calculate descriptive statistics. They will also help you learn ways in which to communicate information about data distributions. O BJECTIVES : Upon successful completion of this activity, you will be able to…  Calculate descriptive statistics using calculator and software  Describe a distribution of values  Find the 5-number summary of a data set and draw a box plot by hand  Use JMP to analyze data sets  Use JMP to draw multiple box plots on the same axis  Compare two distributions D IRECTIONS : Please answer the following questions. When requested show your work. When you are asked to explain an answer use complete sentences. Provide any requested output from JMP. Instructions for creating several types of graphs or tables and statistics can be found on Canvas in the file JMP Instructions.docx . Place your answers and output into this document. You may delete the JMP instructions prior to submitting. Part One 1. (18 points) More Candy Bars. We will calculate several descriptive statistics for the Candy Bars data set from the Section 2 lab. We will do our calculations by hand and using the 1-Var Stats function in your calculator. We will then use JMP to double check our work. a) So that you have less data values to enter into your calculator, take a random sample of size 10 from the full data set. (2 pts) Step 1: Open the Candy Bars data set in JMP Select Help >> Sample Data Folder and choose the data file Candy Bars . Now go to Tables >> Subset . 1

STAT 3090 S ECTION 3 L AB S PRING 2024 Step 2: In the section for Rows , select Random-sample size: enter 10 for the Random sample size. Select OK . Step 3: Take a screen shot of your data table showing at least the first 5 columns. Paste your data table below. b) What is the mode of the variable sugars from your sample? If there is no mode, simply state that. Remember to include units . (2 pts) c) Using your sample, calculate the mean amount of sugars in the sample of candy bars by hand. Include the symbol for a sample mean and units in your answer. Show your work by filling in the formula for the mean. You may type your formula or handwrite it and insert a picture of it into this document. (2 pts) d) Using your sample calculate the range . Include units in your answer. (2 pts) e) Show how to fill in the formula to calculate the variance of the variable sugars using your sample data. Include the symbol for a sample variance . You do not need to calculate this value by hand. In the next step we will use the calculator to find the value. (2 pts) f) Carefully enter your sample data into a list in your calculator and use the 1-Var Stats function to help you calculate the sample variance . Include units with your answer. Your calculator will provide you with the value of the sample standard deviation. Make the appropriate adjustment to get the variance. (2 pts) Sample standard deviation: Sample variance: 2

STAT 3090 S ECTION 3 L AB S PRING 2024 g) Interpret the value of the standard deviation in the context of this data. (2 pts) h) Use JMP to calculate the descriptive statistics for your sample. (2 pts) Step 1: Go to Analyze >> Distribution . Make sure to do it on your sample, not the entire dataset. Step 2: Put the column for sugars into Y, Columns and select OK . (The screen shot used a different column, be sure to use sugars column) Step 3: Change the orientation of the output to a horizontal format. To do this, select the triangle to the left of the word Distributions in your output and choose Stack . Step 4, Change the summary statistics to display the variance and range as well. Select the red triangle next to the Summary Statistics Table and then choose Customize Summary Statistics . Select the variance and range from the list of choices. Copy and paste the resulting Summary Statistics Table below. 3

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STAT 3090 S ECTION 3 L AB S PRING 2024 i) Check your calculations for parts c), d) and f) against your JMP results. If they do not match, figure out where you made your mistake and correct it. Type DONE below when you have checked your work and everything is correct. (2 pts) 2. WebAssign questions 1 - 3. (12 points) Part Two 3. (20 points) Cheerio Many manufacturing processes produce data that is approximately normally distributed (mound or bell shaped, symmetric and unimodal). Suppose the machine that fills Cheerios boxes is set to have a mean box weight of 21 oz and a standard deviation of 0.4 oz. The JMP file Cheerio Box Weights contains the weights of 115 randomly selected boxes each of cereal that Delectable Delights prepared for 2 shipments. a) Observe the column of Shipment 1. Note that the data in Shipment 1 are already ordered increasingly. Find the 5-number summary of this Shipment 1 data set by hand. (2 pts) b) Calculate IQR , lower fence , and upper fence by hand using the 5-number summary in Question 1. Determine whether there are any outliers . (2 pts) c) Draw a box plot by hand for this data set using what you obtained from Question 1 and Question 2. (2 pts) d) Interpret the IQR you obtained from Question 2 based on the context. (2 pts) e) Now let’s use JMP to analyze the data. Use JMP to draw a histogram along with quantiles table and summary statistics for the sample from shipment 1. (2 pts) Step 1, create a histogram: Go to Analyze >> Distribution. Put the column for Weight (oz) Shipment 1 into Y, Columns and select OK. Change the orientation of 4

STAT 3090 S ECTION 3 L AB S PRING 2024 the output to a horizontal format. To do this, select the triangle to the left of the word Distributions in your output and choose Stack . Step 2, modify axis/labels: For y-axis, click the red triangle to the left of the column heading (in this case it is Weight (oz) Shipment 1). Select Histogram Options >> Count Axis or Prob Axis . This will place either the frequency or relative frequency axis on the histogram depends on what you want to plot. Once more click the red triangle and select Display Options >> Axes on Left to change the location of y-axis. Change the label of the y-axis to Frequency instead of Count, or Relative Frequency instead of Probability by single clicking on the default label. For x-axis, right click on the values on x-axis and select Add Axis Label , then enter the name “Weight (oz) Shipment 1”. (Optional) Step 3, aesthetics: If you would like to change the color of the bars, right click in the white space around the bars and select Histogram Color . Note, we cannot separate bars in histogram for quantitative data as what we did in bar chart for qualitative data, since x-axis is a continuous axis now. Step 4, copy/paste your result: Copy and paste all histogram, quantiles, and summary statistics here. You can use screenshot. (2 pts) f) Using the Quantiles Table of your output from Question 5 , find the percentage of the boxes in Shipment 1 with weights between 20.532 oz to 21.514 oz. Show your calculation. (2 points) g) Describe the distribution of the weights from the sample of the boxes of cereal. Remember to discuss the shape , center , and variability , and unusual values (if there are any). Be careful with the usage of resistant or non-resistant measures based on the shape of distribution. Include units where appropriate. (3 pts) h) Suppose we believe the distribution is approximately symmetric. Use the empirical rule to fill in the following blanks: (3 pts) - _____% of the boxes in Shipment 1 will have weights between 20.57 to 21.33 oz. - 95% of the boxes in Shipment 1 will have weights between _____ to _____ oz. i) Do you believe that the machine that filled the boxes in this sample from shipment 1 was working correctly? Why? (Hint: compare the statistics you got with the 5

STAT 3090 S ECTION 3 L AB S PRING 2024 parameters for the machine. Also, recall that if a distribution is symmetric as is the case with the normal distribution, the mean and median is the same (2 pts) 4. (12 points) Oh No Cheerio Harold is an employee who works in the shipping department. As he was preparing shipment 2, he felt that the boxes of cereal seemed lighter than usual. You are asked to compare a random sample of 115 boxes of cereal from shipment 2 to the sample from shipment 1. (2 pts) a) Step 1: Go to Graph >> Graph Builder . Choose Box Plot at top of graph builder. Step 2: Highlight both samples, then drag them to the x-axis. (How to highlight both samples: select one sample, then hold the shift key to select the second.) Step 3: On the left select the box for the 5 number summary. 6

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STAT 3090 S ECTION 3 L AB S PRING 2024 Step 4: Right click on the white space on graph and select Edit >> Copy Graph , then paste it here. (2 pts) b) Write a few sentences to compare the shape, centers, variability and any unusual features for the two box plots using the output provided by JMP. (8 pts) c) Do you think that the machine that filled the boxes for the second shipment may be malfunctioning? Explain. (2 points) 5. Complete Section 3 WebAssign. (38 points) 7

Section 3 Lab Document (1)-1

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