Q: Suppose the population of adult male hip widths is normally distributed with mean $$\mu = 14.3 in. $$and standard deviation $$\sigma = 0.9 in. $$What is the probability that a randomly selected male has a hip width greater than 16.0 in.?

$$1 - \text{NORM.DIST}(16, 14.3, 0.9, 1) = 0.0295$$

Question 1

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

Accepted Answer

Sample variance $$s^2$$

Question 2

Suppose the population of adult male hip widths is normally distributed with mean $$\mu = 14.3 in. $$and standard deviation $$\sigma = 0.9 in. $$What is the probability that a randomly selected male has a hip width greater than 16.0 in.?

Accepted Answer

$$1 - 	ext{NORM.DIST}(16, 14.3, 0.9, 1) = 0.0295$$

Question 3

A sample of size $$n = 106 is $$drawn from a population with mean $$\mu = 98.6$$ and standard deviation $$\sigma = 0.62. $$What is the standard error of the mean?

Accepted Answer

$$\sigma_{\bar{x}} = \frac{0.62}{\sqrt{106}} = 0.0602$$

Question 4

Which of the following is NOT a requirement for using the normal distribution to approximate the sampling distribution of the sample mean $$\bar{x}$$?

Accepted Answer

The population mean must be known

Question 5

If the population is not normally distributed and $$n \leq 30$$, what can be said about the distribution of the sample mean $$\bar{x}$$?

Accepted Answer

It cannot be well approximated by a normal distribution

Question 6

A researcher rolls a fair die 5 times and records the proportion of odd numbers. If this process is repeated many times, what is the expected shape of the distribution of sample proportions?

Accepted Answer

Approximately normal

Question 7

Which of the following best describes the Rare Event Rule for Inferential Statistics?

Accepted Answer

If an observed event is very unlikely under an assumption, the assumption is probably not correct

Question 8

Given a population proportion $$p$$ and a sample proportion $$\hat{p}$$, which of the following is true?

Accepted Answer

The mean of all sample proportions $$\hat{p}$$ equals the population proportion $$p$$

Question 9

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

Accepted Answer

Sample standard deviation $$s$$

Question 10

A sample of 106 body temperatures has a mean of 98.2°F. If the population mean is 98.6°F and the population standard deviation is 0.62°F, what is the $$z-$$score for the sample mean?

Accepted Answer

$$z = \frac{98.2 - 98.6}{0.62/\sqrt{106}}$$

Question 11

Why is the result from part (a) of the Boeing 737 seat width example more relevant for seat design than the result from part (b)?

Accepted Answer

Because individual seats are occupied by individual passengers, not groups

Question 12

Which of the following is the correct formula for the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

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

Question 13

If the probability of obtaining a sample mean as extreme as the observed value is extremely low under the null hypothesis, what is the most reasonable conclusion?

Accepted Answer

The null hypothesis is probably not correct

Question 14

Which of the following is true about the distribution of sample variances?

Accepted Answer

Sample variances tend to have a skewed distribution

Question 15

A population has mean $$\mu$$ and standard deviation $$\sigma. If $$all possible samples of size $$n$$ are taken, what is the mean of the sampling distribution of the sample mean $$\bar{x}$$?

Accepted Answer

$$\mu_{\bar{x}} = \mu$$

Question 16

Which of the following is a correct interpretation of a very low probability for a sample mean under the assumption that the population mean is correct?

Accepted Answer

It is more reasonable to conclude that the population mean is not correct

Question 17

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

Accepted Answer

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

Question 18

Which of the following statements about the sample standard deviation $$s is $$true?

Accepted Answer

$$s is a $$biased estimator of $$\sigma$$, but the bias is small for large samples

Sampling Distributions and Estimators: Concepts, Properties, and Applications

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