Also need an explanation of why each is true or false Questions 1 through 9: Tel

Question

Also need an explanation of why each is true or false Questions 1 through 9: Tell each of the following statements is true or false. Let µ represent the population mean, p the population proportion, x the sample mean, and p ˆ the sample proportion. Assume that all samples are drawn completely random. (3pts each) 1. The binomial random variable is a continuous random variable. 1. 2. The probability density function can be greater than 1. 3. The probability density function can be negative. 4. The cumulative distribution function can be greater than 1. 5. A statistic is any quantity whose value can be calculated from sample data. 6. x is a statistic. 7. p ˆ is an unbiased estimate of p. 8. When the sample size is sufficiently large, p ˆ has approximately a uniform distribution. 9. When the sample size is sufficiently large, µ has approximately a normal distribution

Explanation / Answer

1. False, binomial random variable is a discrete random variable.

2. False, the probability density function cannot be greater than 1.

3. False, the probability density function cannot be negative.

4. False, the cumulative distribution function cannot be greater than 1.

5. True

6. True

7. True

8. False, when the sample size is sufficiently large, p ˆ has approximately a normal distribution.

9. False, when the sample size is sufficiently large, µ can have any distribution.

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