Question 1

Which of the following best describes a sampling distribution?

Accepted Answer

The probability distribution of all possible values of a sample statistic calculated from samples of a fixed size from a population.

Question 2

A sample statistic is considered an unbiased estimator of a population parameter if:

Accepted Answer

The mean of its sampling distribution equals the population parameter.

Question 3

Suppose the population mean $$\mu = 100$$ and the population standard deviation $$\sigma = 20. If $$you take a random sample of size $$n = 25$$, what is the standard error of the sample mean?

Accepted Answer

$$4$$

Question 4

According to the Central Limit Theorem, as the sample size $$n$$ increases, the sampling distribution of the sample mean:

Accepted Answer

Becomes approximately normal, regardless of the population's distribution.

Question 5

Which formula gives the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

$$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$$

Question 6

A company produces soda cans with a mean fill of $$12 oz $$and a standard deviation of $$0.2 oz. If a $$random sample of $$50$$ cans is selected, what is the probability that the sample mean is less than $$11.95 oz$$? (Assume normality.)

Accepted Answer

$$0.0384$$

Question 7

Which of the following is NOT a property of an unbiased estimator?

Accepted Answer

Its expected value is always less than the population parameter.

Question 8

If the sample proportion $$\hat{p} is $$used to estimate the population proportion $$p$$, what is the standard deviation of the sampling distribution of $$\hat{p}$$?

Accepted Answer

$$\sqrt{\frac{p(1-p)}{n}}$$

Question 9

A population has mean $$\mu = 60$$ and standard deviation $$\sigma = 12. If $$you take a sample of size $$n = 36$$, what is the probability that the sample mean is between $$58$$ and $$62$$? (Assume normality.)

Accepted Answer

About $$0.8664$$

Question 10

Which of the following statements about the Central Limit Theorem is FALSE?

Accepted Answer

It requires the population to be normally distributed for any sample size.

Question 11

Which of the following is a point estimator for the population mean $$\mu$$?

Accepted Answer

The sample mean $$\bar{x}$$

Question 12

If a sample statistic has the smallest variance among all unbiased estimators of a parameter, it is called:

Accepted Answer

Minimum-variance unbiased estimator (MVUE)

Question 13

A population is not normally distributed. According to the Central Limit Theorem, what is the minimum sample size $$n$$ generally considered sufficient for the sampling distribution of the sample mean to be approximately normal?

Accepted Answer

$$n \geq 30$$

Question 14

Which of the following is true about the mean of the sampling distribution of the sample mean?

Accepted Answer

It is equal to the population mean $$\mu.$$

Question 15

A random sample of $$n = 100 is $$taken from a population with $$p = 0.4. $$What is the standard error of the sample proportion?

Accepted Answer

$$0.049$$

Question 16

Which of the following best describes the relationship between sample size and the standard error of the mean?

Accepted Answer

As sample size increases, the standard error decreases.

Question 17

A sample mean is calculated from a sample of size $$n = 36$$ from a population with $$\mu = 80$$ and $$\sigma = 18. $$What is the probability that the sample mean is greater than $$83$$? (Assume normality.)

Accepted Answer

About $$0.0475$$

Question 18

Which of the following is NOT a characteristic of a sampling distribution?

Accepted Answer

It is the distribution of the population data.

Sampling Distributions: Foundations and Applications in Business Statistics

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