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One-Sample Tests of
Hypothesis
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What is a Hypothesis?
It is a statement about a population parameter
Hypothesis Testing It’s a procedure based on sample evidence and
probability theory to determine whether the
hypothesis is a reasonable statement
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Five-Step Procedure for Testing a
Hypothesis
State null and alternate hypothesis
Select a level of significance
Identify the test statistic Formulate a decision rule
Take a sample, arrive at decision
Do not reject H 0
Reject H 0 and accept H 1
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State null and alternate hypothesis
Null Hypothesis
It’s a statement about the value of a population
parameter
Alternate Hypothesis
It’s a statement that is accepted if the sample data
provide enough evidence that the null hypothesis is
false
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Select a level of significance
Level of significance
It’s the probability of rejecting the null hypothesis when it is true
TYPE I ERROR
Rejecting the null hypothesis, H 0, when it is true
TYPE II ERROR
Accepting the null hypothesis when it is false
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Identify the test statistic
Test Statistic
It is a value, determined from a sample
information, used to determine whether to reject
the null hypothesis
z – Distribution as a test statistic
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Formulate a decision rule
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Make a Decision
One-Tailed Tests of Significance
Two-Tailed Tests of Significance
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Example 1
The Jamestown Steel Company manufactures and assemblesdesks and other office equipment at several plants in western
New York State. The weekly production of the Model A325
desk at the Fredonia Plant is normally distributed, with a mean
of 200 and a standard deviation of 16. Recently, due to marketexpansion, new production methods have been introduced
and new employees hired. The vice president of
manufacturing would like to investigate whether there has
been a change in the weekly production of the Model A325desk. To put it another way, is the mean number of desks
produced at the Fredonia Plant different from 200 at the 0.01
significance level? Assuming a 50 weeks sample mean of 203.5
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Example 2
The Thompson’s Discount Appliance Store
issues its own credit card. The credit manager
wants to find whether the mean monthly unpaid
balance is more then $400. The level of
significance is set at 0.05. A random check of
172 unpaid balances revealed the sample mean is
$407 and the standard deviation of the sample is$38. Should the credit manager conclude the
population mean is greater than $400?
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Example 3
The McFarland Insurance Company ClaimsDepartment reports that the mean cost to process aclaim is $60. An industry comparison showed thisamount to be larger than most other insurance
companies, so they instituted cost-cutting measures. Toevaluate the effect of the cost-cutting measures,McFarland selected a random sample of 26 recentclaims. The mean cost per claim was $57 and thestandard deviation was $10. Can they conclude that the
cost-cutting measures were effective? Or should they conclude that the difference between the sample mean($57) and the population mean ($60) is due to chance?Use the 0.01 significance level
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Example 4
The mean length of a small counterbalance bar is 43millimeters. The production supervisor is concernedthat the adjustments of the machine producing the barshave changed. He asks the Engineering Department to
investigate. Engineering selects a random sample of 12bars and measures each. The results are reported below in millimeters.
Is it reasonable to conclude that there has been achange in the mean length of the bars? Use the 0.02significance level.
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