MATH399 Week 4 Lab [StatCrunch]: Questions and Answers

Calculating Binomial Probabilities  Open a new StatCrunch worksheet. Click Multimedia Library under Course Home and check the StatCrunch checkbox before clicking Find. Click on ANY given chapter for StatCrunch, and then click Open StatCrunch near the top of your screen INSTEAD of any of the chapter data files.  Change var1 to X, and enter 0 through 10 in the column below. Click the Data button, then from that menu Compute, then Expression, then Build.  Scroll down through the function list to dbinom and double click it. Double click the X in the Column list on the left of the function listing. Arrow over once and type the number 10, then arrow over one more time and type the number 0.5. Click Okay, then Compute.  You should see a column header with the dbinom function and it parameters (x,n,p).  Repeat for p = 0.25 and p = 0.75. In each case, you should be able to simply edit the previous expression when it pops up in the Expression menu. Plotting the Binomial Probabilities 1. Create plots for the three binomial distributions above. Change each of the header labels to “P(X) for p = .5”, “P(X) for p = .25”, and “P(X) for p = .75”, accordingly. Click the Graph button and choose Scatter Plot. Select X for the X variable and P(X) for p = .25 for the Y variable, then Compute, and a graph will appear on screen. Repeat for the other two columns. Right-click each graph and save the image to your computer. Use the Insert menu in Word to browse for those images and insert them into the box below. Do this for each graph image. (12 points) Calculating Descriptive Statistics  You will use the same class survey results that were in the Week 2 iLab Assignment. Find that spreadsheet and copy the entire Coin column into a blank column in StatCrunch. Be sure to copy the column header from that spreadsheet along with its data, and then paste it over one of the var-named headers in StatCrunch, such as var5 or var6—if they are still empty. 2. Calculate descriptive statistics for the variable (Coin) where each of the students flipped a coin 10 times. Click the Stat button, then Summary Stats, Columns. Select the Coin column name by clicking it once so that it populates the right-hand field of that panel. In the Statistics section of this control panel, click Mean, then CTRL-click Std. dev. Click Compute. Enter the data below. (4 points) Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions. Round all numeric values to three decimal places. 3. List the probability value for each possibility in the binomial experiment that was calculated in StatCrunch with the probability of a success being ½. (Complete sentence not necessary; round your answers to three decimal places) (10 points) 4. Give the probability for the following based on the StatCrunch calculations with the probability of a success being ½. The Binomial Calculator function on the Stat button menu will help you avoid careless arithmetic error that might come by doing the following calculations manually. Click Stat, then Calculators, and Binomial. A graph should appear with input options for n and p. Enter 10 for n, and 0.5 for p. Click the inequality symbol and select the appropriate version for each input below. HINT: The Between button at the top of the panel will help you with one of these, but be careful and think your way through its limitation, and one of these will require a manual computation of two separate values. (Complete sentence not necessary; round your answers to three decimal places) (12 points) 5. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ½ and n = 10. Either show work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = 6. Using all four of the properties of a Binomial experiment (see page 201 in the textbook) explain in a short paragraph of several complete sentences why the Coin variable from the class survey represents a binomial distribution from a binomial experiment. (4 points) 7. Compare the mean and standard deviation for the Coin variable (question 2) with those of the mean and standard deviation for the binomial distribution that was calculated by hand in question 5. Explain how they are related in a short paragraph of several complete sentences. (4 points)