Question 1

Which of the following best describes a parameter in statistics?

Accepted Answer

A value that describes a characteristic of a population, such as the population mean

Question 2

A statistic is considered unbiased if:

Accepted Answer

Its expected value equals the parameter it estimates

Question 3

The mean of the sampling distribution of $$\bar{x} is$$:

Accepted Answer

$$\mu$$

Question 4

According to the Central Limit Theorem (CLT), the sampling distribution of $$\bar{x} is $$approximately normal when:

Accepted Answer

$$n \u003e 30$$

Question 5

The standard error of the mean is given by:

Accepted Answer

$$\sigma/\sqrt{n}$$

Question 6

A 95% confidence interval corresponds to which $$z-$$value?

Accepted Answer

1.96

Question 7

When constructing a confidence interval for the mean with a small sample size and unknown population standard deviation, which distribution should be used?

Accepted Answer

t-distribution

Question 8

If you increase the sample size while keeping all else constant, what happens to the width of a confidence interval for the mean?

Accepted Answer

It decreases

Question 9

The center of the sampling distribution of $$\bar{x} is$$:

Accepted Answer

$$\mu$$

Question 10

A point estimator produces:

Accepted Answer

A single number

Question 11

Given a population with $$\mu = 80$$, $$\sigma = 12$$, and a sample size $$n = 36$$, what is the standard error of the mean?

Accepted Answer

$$2$$

Question 12

Suppose you have a sample mean $$\bar{x} = 50$$, population standard deviation $$\sigma = 10$$, and $$n = 64. $$What is the 95% confidence interval for $$\mu$$?

Accepted Answer

$$50 \pm 1.96 	imes (10/8)$$

Question 13

Which of the following will NOT reduce the width of a confidence interval for the mean?

Accepted Answer

Increasing the population standard deviation

Question 14

A business wants to estimate the average time customers spend in their store. They collect a sample of 16 customers with $$\bar{x} = 50$$ minutes and $$s = 14.5$$ minutes. What is the appropriate distribution and critical value for a 90% confidence interval?

Accepted Answer

t-distribution, $$t_{0.05,15} \approx 1.753$$

Question 15

Given $$\mu = 25$$, $$\sigma = 5$$, $$n = 100$$, what is $$P(\bar{x} \u003e 26)$$?

Accepted Answer

$$P(z \u003e 2)$$

Question 16

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a fixed value for a population; a statistic is a variable value from a sample

Question 17

What does the Central Limit Theorem (CLT) allow us to do in practice?

Accepted Answer

Use the normal distribution to approximate the sampling distribution of the sample mean for large samples

Question 18

What is the confidence coefficient for a 95% confidence interval?

Accepted Answer

0.95

Question 19

As the sample size $$n$$ approaches infinity, what happens to the standard error of the mean?

Accepted Answer

It decreases to zero

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