Questions 1: State YES or NO for each statement in the brackets provided. Let µ

Question

Questions 1: State YES or NO for each statement in the brackets provided. Let µ represent the population mean, p the population proportion, x the sample mean, and pˆ the sample proportion. Assume that all samples are randomly and independently drawn.

• ( ) The probability density function can be greater than 1.

• ( ) The probability density function can be negative.

• ( ) The cumulative distribution function can be greater than 1.

• ( ) A statistic is any quantity whose value can be calculated from sample data.

• ( ) x is a statistic.

• ( ) pˆ is a parameter.

• ( ) x is always normally distributed when the sample size is sufficiently large.

• ( ) µ is always normally distributed when the sample size is sufficiently large.

• ( ) H0 :µ =100 vs H A :µ 100 is a legitimate hypothesis set. • ( ) H0 :x =100 vs H A :x 100 is a legitimate hypothesis set.

Explanation / Answer

1) (Yes ) The probability density function can be greater than 1.

2)  (No ) The probability density function can be negative.

3)  (No ) The cumulative distribution function can be greater than 1.

4)  ( Yes) A statistic is any quantity whose value can be calculated from sample data

5)  (Yes ) x is a statistic.

6)  ( No) pˆ is a parameter.

7)  (Yes ) x is always normally distributed when the sample size is sufficiently large.

8)  ( No) µ is always normally distributed when the sample size is sufficiently large.

9)( yes) H0 :µ =100 vs H A :µ 100 is a legitimate hypothesis set. •

10)  ( No) H0 :x =100 vs H A :x 100 is a legitimate hypothesis set.

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