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F Distribution and ANOVA: Practice

Module by: Dr. Barbara Illowsky, Susan Dean

Summary: This module provides a practice on F Distribution and ANOVA as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

Student Learning Outcome

  • The student will explore the properties of ANOVA.

Given

Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.

  Northeast South West Central East
  16.3 16.9 16.4 16.2 17.1
  16.1 16.5 16.5 16.6 17.2
  16.4 16.4 16.6 16.5 16.6
  16.5 16.2 16.1 16.4 16.8
x ¯ = x ¯ = size 12{ {overline {x}} ={}} {} ________ ________ ________ ________ ________
s 2 = s 2 = size 12{s rSup { size 8{2} } ={}} {} ________ ________ ________ ________ ________

Hypothesis

Exercise 1

State the hypotheses.

HoHo size 12{H rSub { size 8{O} } } {}:

HaHa size 12{H rSub { size 8{a} } } {}:

Data Entry

Enter the data into your calculator or computer.

Exercise 2

degrees of freedom - numerator: df(n)=df(n)= size 12{ ital "df" \( n \) ={}} {}

Solution 2

d f ( 1 ) = 4 df(1)=4

Exercise 3

degrees of freedom - denominator: df(d)=df(d)= size 12{ ital "df" \( d \) ={}} {}

Solution 3

d f ( 2 ) = 15 df(2)=15

Exercise 4

F test statistic =

Solution 4

Test statistic = F = 4.22=F=4.22

Exercise 5

p-valuep-value =

Solution 5

0.017

Decisions and Conclusions

State the decisions and conclusions (in complete sentences) for the following preconceived levels of αα size 12{α} {} .

Exercise 6

α=0.05α=0.05 size 12{α=0 "." "05"} {}

Decision:

Conclusion:

Exercise 7

α = 0 . 01 α = 0 . 01 size 12{α=0 "." "01"} {}

Decision:

Conclusion:

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