1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Chapter 7 Technology

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.1: Using a TI-83/84 Plus Calculator to Calculate the Standard Score for a Sample Mean Find the value of z for the sample mean using the formula from the Central Limit Theorem given that Solution The formula we need is the equation of the z-value for a sample mean in a sampling distribution from the Central Limit Theorem. Let’s begin by substituting the given values into the equation.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.1: Using a TI-83/84 Plus Calculator to Calculate the Standard Score for a Sample Mean (cont.) Now we need to enter this into the calculator. We must make sure that we put parentheses around the numerator and the denominator.

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.1: Using a TI-83/84 Plus Calculator to Calculate the Standard Score for a Sample Mean (cont.) Enter the following into the calculator: (34Þ35)/(5/ð(100)). Press. Thus, z =  2.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.2: Using a TI-83/84 Plus Calculator to Calculate the Standard Score for a Sample Proportion Find the value of z for the sample proportion using the formula from the Central Limit Theorem given that Solution The formula we need is the equation of the z-value for a sample proportion in a sampling distribution from the Central Limit Theorem. Let’s begin by substituting the given values into the equation.

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.2: Using a TI-83/84 Plus Calculator to Calculate the Standard Score for a Sample Proportion (cont.) Now we need to enter this into the calculator. We must make sure that we put parentheses around the numerator and the denominator.

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.2: Using a TI-83/84 Plus Calculator to Calculate the Standard Score for a Sample Proportion (cont.) Enter the following into the calculator: (0.56Þ0.54)/ ð(0.54(1Þ0.54)/81). Press. Thus, z ≈ 0.36.

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.3: Using Microsoft Excel to Calculate the Standard Score for a Sample Mean Find the value of z for the sample mean using the formula from the Central Limit Theorem given that Solution Recall that the Central Limit Theorem states that the standard deviation of a sampling distribution of sample means, equals the standard deviation of the population divided by the square root of the sample size.

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.3: Using Microsoft Excel to Calculate the Standard Score for a Sample Mean (cont.) That is, The formula for calculating the value of z in Microsoft Excel is =STANDARDIZE(x, mean, standard_dev). Applying the Central Limit Theorem, we input =STANDARDIZE(34, 35, 5/SQRT(100)). Just as we found in Example T.1, z = −2.

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Calculate the Standard Score for a Sample Find the value of z for the sample proportion using the formula from the Central Limit Theorem given that Solution Here we will use Enter =STANDARDIZE(0.56, 0.54, SQRT(0.54*(1-0.54)/81)) into Excel. The answer, 0.361158, is displayed. Thus, z ≈ 0.36.

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.5: Using M INITAB to Calculate Standard Scores for Sample Means The call processing times at an emergency dispatch center have a population mean of 45 seconds and a standard deviation of 50 seconds. Five operators are evaluated using random samples of the calls they have handled. The total number of calls sampled and the corresponding mean processing time for each operator are displayed in the table below. Find the z-score for each sample mean. Call Processing Times (in Seconds) n9885105110 91 Sample Mean52486345 55

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.5: Using M INITAB to Calculate Standard Scores for Sample Means (cont.) Solution First, enter the data into columns C1 and C2 in the worksheet. The first column is n, the number of calls sampled, and the second column contains each operator’s sample mean. Go to Calc ► Calculator and enter the following expression: (C2-45)/(50/SQRT(C1)). Choose to store the result in column C3 and click OK. The dialog box appears as follows.

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.5: Using M INITAB to Calculate Standard Scores for Sample Means (cont.)

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.5: Using M INITAB to Calculate Standard Scores for Sample Means (cont.) The column produced contains the z-score for each operator.