hyp testing handout

8/11/2019 Hyp Testing Handout

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Cathy Chen Marketing Research Term 1, 2014-15

Hypothesis Testing

Hypothesis testingis a procedure used to check whether or not astated orassumedbeliefabout an underlying population or process is supported by the data.

The Steps of Hypothesis Testing

Step 1.Problem Definition

Step 2. Form the Null and Alternative Hypotheses

Thestated orassumed beliefis called the null hypothesis(usually assume equalto expectation, or not different from zero). The other option (which is perhapswhat data has been telling us) is that the assumed belief may not be true and is

called the alternative hypothesis.

Step 3. Choose the relevant test and compute the Test Statistic

Based on the types of question and scales, you can choose the appropriateprobability distribution and test. For example, nominal variables often involvechi-square test. Interval and ratio-scaled variables can be analyzed using t test, z

test, F test etc. For specific test, please refer to class examples and the table onpage 3.

What is the data telling you?

Compute the sample statistic. The decision-maker computes the sample statistic

based on the sample data and calculates how much the sample statistic differsfrom the presumed distribution that is established by the null hypothesis.

Step 4: Choose the critical value based ona. Significance LevelTwo ways to look at the significance level: 1) significance level = 1 confidence

level. That is, 5% significance level corresponds to 95% confidence level. 2) The

significance level is the maximum acceptable error, !. The decision-maker mustelect how much error he/she is willing to accept in making an inference about the

population from the sample data. (Note: The significance level is the maximumprobability that the null hypothesis will be rejected incorrectly, i.e. Type I error).

b. Degree of freedomThis is usually determined by the sample size as well as the parameters to be

estimated. Specifics please refer to the class examples.

c. One-tailed or two-tailed testIf HAis concerned with > or < (i.e., violations from H0in one direction, it would

be a one-tailed test. If HAis interested in (i.e., violations from H0in bothdirections), it would be a two-tailed test.


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Step 5. Compare the Test Statistic with the Critical Value and Make the Decision.

Based on the comparison, the decision-maker will:

Reject the null hypothesis if the absolute value of the sample statistic is larger

than the critical value. This implies that the evidence is so strong that the sample

statistic is very unlikely if the null hypothesis is true. Therefore, the data does notsupport the null hypothesis and we will instead believe HAis true.

Fail to reject the null hypothesis if the absolute value of the sample statistic issmaller than the critical value.

Conclusion: State what the decision means in terms of the business situation.


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Table for testing Means and Proportions

Type of test Null

Hyp.

Alt Hyp. Test statistic (actual) Rejection Region

Single Mean

(Two-sided)= 0 "0 ( )0Xt

s

n

!

= | tactual| > t!/2

Single Mean

(One-sided)

1. = 0 > 0 Same as above tactual> t!

2. = 0 < 0 Same as above tactual< -t!

Comparing

Two Means(Two-sided)

1= 2 1 "2 ( )1 22 2

1 2

1 2

X X

t

s s

n n

!

=

+

| tactual| > t!/2

ComparingTwo Means

(One-sided)

1. 1= 2 1> 2 Same as above tactual> t!

2. = 0 1 < 2 Same as above tactual< -t!

Single

Proportion

(Two-sided)

#= #0 #"#0( )

( )n

pp

pz

o

!

!

=

1

"

| zactual| > z!/2

Single

Proportion

(One-sided)

1. #= #0 #> #0 Same as above zactual> z!

2. #= #0 #< #0 Same as above zactual< -z!

Comparing

TwoProportions(Two-sided)

#1= #2 #1"#2z =

p1!p

2( )p(1!p)

n1

+

p(1!p)

n2

where

p =n

1p

1( )+ n2p2( )n

1+n

2

| zactual| > z!/2

hyp testing handout

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