Math Problem Statement

Find the test statistic.

F Subscript STATequals=3.363.36

​(Round to two decimal places as​ needed.)

Part 3

Determine the​ p-value.

​p-valueequals=0.0120.012

​(Round to three decimal places as​ needed.)

Part 4

Reach a decision.

Reject

H Subscript 0.

There is

sufficient

evidence at the

0.050.05

level of significance of a difference in the mean U.S. average sales per unit among the food segments.

Part 5

b. At the

0.050.05

level of​ significance, is there a difference in the variation in U.S. average sales per unit​ ($ thousands) among the food​ segments? Determine the hypotheses. Choose the correct answer below.

A.

H Subscript 0​:

sigma Subscript 1 Superscript 2σ21equals=sigma Subscript 2 Superscript 2σ22equals=times•times•times•equals=sigma Subscript 48 Superscript 2σ248

H Subscript 1​:

Not all

sigma Subscript j Superscript 2σ2j

are equal

       ​ (where

jequals=​1,2,...,4848​)

B.

H Subscript 0​:

sigma Subscript 1 Superscript 2σ21equals=sigma Subscript 2 Superscript 2σ22equals=times•times•times•equals=sigma Subscript 6 Superscript 2σ26

H Subscript 1​:

Not all

sigma Subscript j Superscript 2σ2j

are equal

       ​ (where

jequals=​1,2,...,66​)

Your answer is correct.

C.

H Subscript 0​:

sigma Subscript 1 Superscript 2σ21equals=sigma Subscript 2 Superscript 2σ22equals=times•times•times•equals=sigma Subscript 6 Superscript 2σ26

H Subscript 1​:

sigma Subscript 1 Superscript 2σ21not equals≠sigma Subscript 2 Superscript 2σ22not equals≠times•times•times•not equals≠sigma Subscript 6 Superscript 2σ26

D.

H Subscript 0​:

sigma Subscript 1 Superscript 2σ21equals=sigma Subscript 2 Superscript 2σ22equals=times•times•times•equals=sigma Subscript 48 Superscript 2σ248

H Subscript 1​:

sigma Subscript 1 Superscript 2σ21not equals≠sigma Subscript 2 Superscript 2σ22not equals≠times•times•times•not equals≠sigma Subscript 48 Superscript 2σ248

Part 6

Find the test statistic.

F Subscript STATequals=enter your response here

​(Round to two decimal places as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Hypothesis Testing
ANOVA
F-Test
p-value

Formulas

F_STAT = Largest variance / Smallest variance
p-value calculation based on F-distribution

Theorems

F-distribution
Hypothesis Testing in ANOVA

Suitable Grade Level

Grades 11-12, Undergraduate