Question 1

Which of the following statements best describes the sampling distribution of a statistic?

Accepted Answer

It is the distribution of all values of the statistic when all possible samples of the same size $$n$$ are taken from the same population.

Question 2

Suppose you roll a fair die 5 times and record the proportion of odd numbers in each sample. If you repeat this process many times, what can you say about the distribution of the sample proportions?

Accepted Answer

The sample proportions will be approximately normally distributed with a mean equal to the population proportion.

Question 3

Which of the following is NOT an unbiased estimator of its corresponding population parameter?

Accepted Answer

Sample median

Question 4

If the population mean is $$\mu = 3.5$$ and you repeatedly take samples of size 5 from this population, what is the expected value of the sample mean $$\overline{x}$$?

Accepted Answer

$$3.5$$

Question 5

Which of the following best describes the shape of the sampling distribution of the sample variance $$s^2$$?

Accepted Answer

It is skewed to the right.

Question 6

A researcher wants to estimate the proportion of defective items in a large shipment. She takes many random samples of size $$n$$ and calculates the sample proportion $$\hat{p}$$ for each. What is true about the mean of all these sample proportions?

Accepted Answer

It is equal to the population proportion $$p.$$

Question 7

Which of the following statistics is a biased estimator of its corresponding population parameter?

Accepted Answer

Sample range

Question 8

Why is the sample standard deviation $$s$$ considered a biased estimator of the population standard deviation $$\sigma$$?

Accepted Answer

Because the mean of the sampling distribution of $$s$$ does not equal $$\sigma.$$

Question 9

Which of the following is the correct formula for the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{x}{n}$$

Question 10

A hospital administrator wants to estimate the average length of stay for patients. She takes many random samples of size $$n$$ and calculates the sample mean $$\overline{x}$$ for each. What can be said about the distribution of these sample means?

Accepted Answer

The distribution of sample means tends to be normal, and the mean of the sample means equals the population mean.

Question 11

Which of the following is a property of an unbiased estimator?

Accepted Answer

Its expected value equals the corresponding population parameter.

Question 12

If you repeatedly take samples of size $$n$$ from a population and calculate the sample variance $$s^2$$ for each, what is true about the mean of all these sample variances?

Accepted Answer

It is equal to the population variance $$\$$sigma^2$$.

Question 13

Which of the following is NOT a property of the sampling distribution of the sample mean?

Accepted Answer

It is always skewed to the right.

Question 14

A quality control manager is interested in the variability of product weights. She takes many samples and calculates the sample variance $$s^2$$ for each. What is the expected shape of the distribution of these sample variances?

Accepted Answer

Skewed to the right

Question 15

Which of the following statistics is an unbiased estimator of its corresponding population parameter?

Accepted Answer

Sample variance $$s^2$$

Question 16

In a population where the proportion of defective items is $$p = 0.1$$, what is the expected value of the sample proportion $$\hat{p} if $$you take many samples of size $$n$$?

Accepted Answer

$$0.1$$

Question 17

Which of the following is a correct statement about the sample standard deviation $$s$$?

Accepted Answer

$$s is a $$biased estimator of $$\sigma$$, but is often used to estimate $$\sigma$$ especially for large samples.

Question 18

A statistician is interested in estimating the average income in a city. She takes many random samples and calculates the sample mean $$\overline{x}$$ for each. What is the expected value of $$\overline{x}$$?

Accepted Answer

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

Question 19

Which of the following is the correct formula for the population proportion $$p$$?

Accepted Answer

$$p = \frac{x}{N}$$

Question 20

Which of the following statistics is NOT a biased estimator?

Accepted Answer

Sample proportion $$\hat{p}$$

6.3

Guida di studio - Domande di pratica

Study guide - Flashcard