Question 1

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

Accepted Answer

A parameter is a numerical value that describes the population, while a statistic is a numerical value calculated from a sample.

Question 2

A researcher wants to estimate the average height of all oak trees in a forest. She measures the height of 30 randomly selected oak trees and calculates the mean. In this context, what is the sample?

Accepted Answer

The 30 randomly selected oak trees that were measured.

Question 3

Which of the following scenarios is an example of measurement bias?

Accepted Answer

Using a survey question that asks, 'Do you agree that responsible citizens recycle?'

Question 4

A pollster wants to know the proportion of voters who support a new law. She calls only landline numbers to conduct her survey. What type of bias is most likely introduced?

Accepted Answer

Sampling bias, because not all segments of the population are equally likely to be included.

Question 5

Which of the following statements about the Central Limit Theorem (CLT) is correct?

Accepted Answer

The CLT states that, for large enough sample sizes, the sampling distribution of the sample proportion is approximately normal, even if the population distribution is not normal.

Question 6

A random sample of 200 people is surveyed, and 90 say they prefer tea over coffee. Calculate the sample proportion $$\hat{p}.$$

Accepted Answer

$$\hat{p} = \frac{90}{200} = 0.45$$

Question 7

Suppose a poll of 800 adults found that 520 support a new environmental policy. Calculate the standard error (SE) for the sample proportion.

Accepted Answer

$$SE = \sqrt{\frac{0.52(1-0.52)}{800}} = 0.0177$$

Question 8

A sample of 100 candies contains 28% red candies. The company claims that 25% of all candies are red. Using the Central Limit Theorem, what is the z-score for the observed sample proportion?

Accepted Answer

$$z = \frac{0.28 - 0.25}{\sqrt{\frac{0.25(1-0.25)}{100}}} = 0.6$$

Question 9

A poll of 1200 adults found that 798 wanted Congress to pass a stimulus bill. What is the 95% confidence interval for the proportion of all adults who want Congress to pass the bill?

Accepted Answer

$$(0.6383, 0.6917)$$

Question 10

Which of the following best interprets a 95% confidence interval for a population proportion?

Accepted Answer

We are 95% confident that the true population proportion falls within the interval.

Question 11

A researcher uses convenience sampling by surveying the first 20 people she sees at a coffee shop. What is the most likely consequence of this sampling method?

Accepted Answer

The sample may not be representative of the population, introducing sampling bias.

Question 12

Which of the following is an example of a scenario where the Central Limit Theorem would NOT apply?

Accepted Answer

A sample size of 8 is taken from a highly skewed population.

Question 13

A survey of 60 professional baseball players finds that 15 are left-handed. What is the margin of error (ME) for a 95% confidence interval for the proportion of left-handed players?

Accepted Answer

$$ME = 1.96 	imes 0.0559 = 0.1096$$

Question 14

A Gallup Poll surveyed 1009 adults and found that 595 wanted to lose weight. What is the standard error (SE) for the sample proportion?

Accepted Answer

$$SE = \sqrt{\frac{0.59(1-0.59)}{1009}} = 0.0155$$

Question 15

Which of the following best describes the difference between accuracy and precision in the context of survey sampling?

Accepted Answer

Accuracy refers to how close measurements are to the true value, while precision refers to how consistent repeated measurements are.

Question 16

A random sample of 300 people found that 141 own a cat. What is the estimated standard error for the sample proportion?

Accepted Answer

$$SE = \sqrt{\frac{0.47(1-0.47)}{300}} = 0.02882$$

Question 17

According to an ice cream shop, 60% of people buy chocolate ice cream. What is the probability that at least 62% of a random sample of 300 people buy chocolate ice cream?

Accepted Answer

0.23885

Question 18

A random sample of 100 M&M's contains 24% orange candies. If the true proportion is 20%, what is the probability of observing 24% or more orange candies in a sample of 100?

Accepted Answer

0.15866

Question 19

Which of the following is NOT a condition that must be met for the Central Limit Theorem to apply to sample proportions?

Accepted Answer

The population must be normally distributed.

Chapter 7 Review Guide: Sampling Distributions, Bias, Central Limit Theorem, and Confidence Intervals

Study Guide - Practice Questions

Study Guide - Flashcards