class 06 - hypothesis testing cases

7/30/2019 Class 06 - Hypothesis Testing Cases

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Hypothesis Testing

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Industrial Engineering

Define the following.

Statistical Hypothesis Parameter

p-Value Confidence Intervals

Hypothesis Testing Treatment

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Conditions for using t-test procedure

In using the t-test procedure we make the assumptions:

Both samples are drawn from independent populations that can bedescribed by a normal distribution

The standard deviation or variances of both populations are equal

The observations are independent random variables.

The equal-variance and normality assumptions are easy to checkusing a normal probability plot

Example



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Constructing Normal Probability Plots

We need specialized normal probability plotting paper which is widelyavailable. This is just graph paper with the vertical (or probability) scale.

It is a plot of the cumulative normal probabilities (j 0.5)/n on that scaleversus the rank-ordered observations y(j)

For the unmodified Portland cement mortar bond strength data


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Now if we plot the cumulative probabilities from the next-to-last column of thistable versus the rank-ordered observations from the second column on normal

probability paper.

A normal probability plot can also be constructed on ordinary graph paper byplotting the standardized normal z-scores z(j) against the ranked observations,where the standardized normal z-scores are obtained from


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Hypothesis Testing Cases

NormalityTest


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HypothesisTesting

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Hypothesis Test Cases

Test on Means with

Variance Known

One Population

Two Populations

Variance Unknown

One Population

Two Populations

Test on Variances of Normal Distribution

One Population

Two Populations


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NormalityTest


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Example

HypothesisTesting

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The shelf life of a carbonated beverage is of interest. Ten bottles are randomlyselected and tested, and the following results are obtained

(a) We would like to demonstrate that the mean shelf life exceeds 120 days.Set up appropriate hypotheses for investigating this claim.

(b) Test these hypotheses using a = 0.01. What are your conclusions?

(c) Find the P-value for the test in part (b).

(d) Construct a 99 percent confidence interval on the mean shelf life.


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HypothesisTesting

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(a) We would like to demonstrate that the mean shelf life exceeds 120 days.Set up appropriate hypotheses for investigating this claim.

H0: = 120 H1: > 120

(b) Test these hypotheses using = 0.01. What are your conclusions?

(c) Find the P-value for the test in part (b). P=0.054

class 06 - hypothesis testing cases

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