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Question

Suppose Sony would like to test the hypothesis that

the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users. The following table summarizes sample statistics from each population.

Playstation

Xbox

Sample standard deviation

4.3 years

3.9 years

Sample size

25

28

What is the correct hypothesis​ statement?

H0

0​: sigma Subscript PS Superscript 2

σ2PSequals

=sigma Subscript XB Superscript 2

σ2XB​; H1

1​: sigma Subscript PS Superscript 2

σ2PSnot equals

≠sigma Subscript XB Superscript 2

σ2XB

B.

H0

0​: sigma Subscript PS Superscript 2

σ2PSless than or equals

≤sigma Subscript XB Superscript 2

σ2XB​; H1

1​: sigma Subscript PS Superscript 2

σ2PS ​> sigma Subscript XB Superscript 2

σ2XB

C.

H0

0​: sigma

σSubscript PS

PSless than or equals

≤sigma

σSubscript XB

XB​; H1

1​: sigma

σSubscript PS

PS ​> sigma

σSubscript XB

XB

D.

H0

0​: sigma Subscript PS Superscript 2

σ2PSgreater than or equals

≥sigma Subscript XB Superscript 2

σ2XB​; H1

1​: sigma Subscript PS Superscript 2

σ2PS ​< sigma Subscript XB Superscript 2

σ2XB

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