A Hypothesis Test for Two Population Standard Deviations Is to Be

question 17

Multiple Choice

A hypothesis test for two population standard deviations is to be performed. Independent random samples of sizes $\mathrm { n } _ { 1 }$ and $\mathrm { n } _ { 2 }$ are drawn from the two populations. The variable under consideration is normally distributed on each of the two populations. The test statistic is $\mathrm { s } _ { 1 } ^ { 2 } / \mathrm { s } _ { 2 } ^ { 2 }$ . If the null hypothesis, $\mathrm { H } _ { 0 } : \sigma _ { 1 } = \sigma _ { 2 }$ , is true, what is the distribution of this test statistic?

• A)\(\chi ^ { 2 }\)-distribution with \(\mathrm { df } = \mathrm { n } _ { 1 } + \mathrm { n } _ { 2 } - 1\)
• B) \(\mathrm { F }\)-distribution with df \(= \left( \mathrm { n } _ { 1 } , \mathrm { n } _ { 2 } \right)\)
• C) F-distribution with \(\mathrm { df } = \left( \mathrm { n } _ { 2 } - 1 , \mathrm { n } _ { 1 } - 1 \right)\)
• D) \(F\)-distribution with \(\mathrm { df } = \left( \mathrm { n } _ { 1 } - 1 , \mathrm { n } _ { 2 } - 1 \right)\)

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Definitions:

Secondary Circular Reactions

Secondary circular reactions are a developmental phase in infants, occurring around 4-8 months, characterized by the repetition of actions that produce effects outside the body, showing an early awareness of cause and effect.

Sensorimotor

The first stage in Piaget's theory of cognitive development, where infants learn through interacting with the environment, from birth to about 2 years of age.

Concrete Operational

A stage in cognitive development, according to Piaget, where children gain the ability to think logically about concrete events.

Preoperational

A stage in Jean Piaget's theory of cognitive development during which children aged approximately 2 to 7 years old develop memory and imagination.