hawkes learning systems students matter. success counts. copyright © 2013 by hawkes learning...

HAWKES LEARNING SYSTEMS

Students Matter. Success Counts.

Copyright © 2013 by Hawkes Learning

Systems/Quant Systems, Inc.

All rights reserved.

Chapter 7

Technology






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

SolutionThe 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.

34, 35, 5 100, and .x n






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.

34 355

100

xz

n






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.






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

SolutionThe 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.

ˆ= 0.56, = 0. , and54 = . 81p p n






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.

ˆ 0.56 0.54

1 0.54 1 0.5481

p pz

p pn






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.






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

SolutionRecall 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.

34, = 35, = , and5 = 1 0 0 .x m s n

,x






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.

.x n






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

SolutionHere 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.

ˆ 0.56, = 0.5 , and4 = . 81p p n

ˆ

1.p

p pn






Example T.5: Using MINITAB 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) n 98 85 105 110 91

Sample Mean 52 48 63 45 55






Example T.5: Using MINITAB to Calculate Standard Scores for Sample Means (cont.)

SolutionFirst, 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.







The column produced contains the z-score for each operator.

hawkes learning systems students matter. success counts. copyright © 2013 by hawkes learning...

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sample mean

sample proportion

standard score

success counts

value of z

standard deviation

central limit theorem

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