stat hypothesis

7/30/2019 Stat Hypothesis

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SCHOOL OF BUSINESSUAM PROF: HNVG

One-Sample Tests of

Hypothesis




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




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




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




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




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




Formulate a decision rule




Make a Decision

One-Tailed Tests of Significance

Two-Tailed Tests of Significance




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




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?




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




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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stat hypothesis

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