Question

# Which one is the correct statement? Choose all applied. a. If you are interested in US...

Which one is the correct statement? Choose all applied.

 a. If you are interested in US households, proportion of 500 US households who do not have any health insurance is a point estimate of proportion of all US households who do not have any health insurance. b. If you are interested in US households, mean income of 500 US households is a random variable. c. If you are interested in US households, mean income of 500 US households is a point estimate of mean income of all US households. d. If you are interested in US households, mean income of US households is a fixed number, that is, not a random variable.

Solution:- a, b, c

The correct statements are :

a) If you are interested in US households, proportion of 500 US households who do not have any health insurance is a point estimate of proportion of all US households who do not have any health insurance.

When we select a random sample from the population of interest, we expect the sample proportion to be a good estimate of the population proportion.

b) If you are interested in US households, mean income of 500 US households is a random variable.

The sample mean is a random variable, because its value depends on the particular random sample happens that is chosen.

c) If you are interested in US households, mean income of 500 US households is a point estimate of mean income of all US households.

The expected value of the sample mean is the population mean, and the SE of the sample mean is the SD of the population, divided by the square-root of the sample size. The sample mean of a random sample from a population is an estimator of the mean of the population.

Incorrect statement is:

d) If you are interested in US households, mean income of US households is a fixed number, that is, not a random variable.

The sample mean is a random variable, because its value depends on the particular random sample that is chosen.

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