chapter 7
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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 Solution - PowerPoint PPT PresentationTRANSCRIPT
HAWKES LEARNING SYSTEMS
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Chapter 7
Technology
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
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
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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
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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.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
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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
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
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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
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
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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.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
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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
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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
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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
HAWKES LEARNING SYSTEMS
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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
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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.
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Example T.5: Using MINITAB to Calculate Standard Scores for Sample Means (cont.)
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
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Systems/Quant Systems, Inc.
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Example T.5: Using MINITAB to Calculate Standard Scores for Sample Means (cont.)
The column produced contains the z-score for each operator.