# QMS 202 Chapter Notes -Null Hypothesis, Test Statistic, Standardized Test

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20 Apr 2012

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Question#1

The training director of a manufacturing company wants to compare three

different team-based approaches. Each member of a group of 29 new employees

is randomly assigned to one of three team-based methods. After completing

training, the employees in the study are evaluated on the time it takes (in

minutes) to assemble the product. The results are shown in the following table.

Methods

Time To Assemble Product

A

8.57, 8.50 , 9.11 , 8.20 , 8.32 , 7.88 , 9.90 , 9.43 , 8.75

B

7.98 , 8.40 , 8.84 , 7.75 , 8.20 , 7.95 , 8.21 , 6.65 , 7.44 , 8.33

C

8.70 , 8.82, 9.26, 8.96 , 8.65 , 8.30, 9.46 , 9.43 , 9.26 , 9.02

At the 0.05 level of significance, is there evidence of a significant difference in the

average assembly time among the team-based methods?

a. What type of parameter(s) is being tested here? (Circle one)

ˆ

x

ˆ

s

s

ˆ

ˆ

p

p

ˆ

t

z

F

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b. Define the parameters associated with the test {include the appropriate

symbol(s)}

c. State the hypothesis using statistical symbols.

Null Hypothesis: _____________________________

Alternative Hypothesis: _____________________________

d. What procedure is used to perform this test? (Circle one)

t test z test ANOVA Chi-Square

e. What condition(s) is/are required for this procedure to be legitimate?

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f. Which specific standardized test statistic is used to test this hypothesis?

Indicate the degree of freedom (df) if appropriate.

z

z

df _____________

t

df _____________

t

df _____________ df ____________

F

df _____________

F

df _____________ df ____________

2

df _____________

2

df _____________ df ____________

g. What is the value of the test statistic? ________________

h. What is the critical value(s) for this test? ______________

i. What is the p-value for this test? ________________

j. Construct a graph of the most appropriate distribution clearly showing the

critical value(s), test statistic value, and the rejection region

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k. What is the statistical decision and why?

Reject

A

H

Do not reject

A

H

Reject

0

H

Do not reject

0

H

because the p-value is

than

2/

than

2/

to

2/

than

than

to

than

2

than

2

to

2

l. In non-technical terms what is your conclusion for this test?

m. Name the procedure which must be carried out in order to complete the test.

State the reason why that procedure can be used.