Q: A researcher wants to estimate the proportion of voters who support a candidate. If the true proportion is $$p = 0.6$$ and the sample size is $$n = 100$$, what is the standard deviation of the sampling distribution of $$\hat{p}$$?

$$\sigma_{\hat{p}} = \sqrt{\frac{0.6 \times 0.4}{100}}$$

Question 1

A medical researcher wants to study the effect of a new drug on blood pressure. She randomly assigns 100 patients to either receive the drug or a placebo and measures their blood pressure after 6 weeks. What type of study is this?

Accepted Answer

Experiment

Question 2

Which of the following best describes a simple random sample?

Accepted Answer

A sample where every individual has an equal chance of being selected

Question 3

A survey is conducted by calling randomly generated phone numbers. Which sampling method is being used?

Accepted Answer

Random digit dialing

Question 4

Which of the following is a potential problem with volunteer samples (voluntary response samples)?

Accepted Answer

They often suffer from selection bias

Question 5

In a study, the population is all students at a university, and a sample of 200 students is surveyed about their study habits. Which of the following is a parameter?

Accepted Answer

The mean study hours of all students at the university

Question 6

A researcher wants to compare the effectiveness of two teaching methods. She pairs students based on their prior test scores and randomly assigns one from each pair to each method. What experimental design is this?

Accepted Answer

Matched pairs design

Question 7

Which principle of experimental design is best illustrated by randomly assigning subjects to treatment groups?

Accepted Answer

Randomization

Question 8

A survey question asks: 'Don’t you agree that the new policy is beneficial?' What type of bias might this wording introduce?

Accepted Answer

Response bias

Question 9

If two events $$A$$ and $$B$$ are disjoint (mutually exclusive), what is $$P(A \cap B)$$?

Accepted Answer

$$P(A \cap B) = 0$$

Question 10

A random variable $$X$$ has the following probability distribution: $$P(X=1)=0.2$$, $$P(X=2)=0.5$$, $$P(X=3)=0.3. $$What is the expected value $$E[X]$$?

Accepted Answer

$$E[X] = 2.1$$

Question 11

Which of the following best describes the Central Limit Theorem?

Accepted Answer

The distribution of sample means approaches a normal distribution as sample size increases, regardless of the population distribution.

Question 12

A fair six-sided die is rolled. What is the sample space $$S$$?

Accepted Answer

$$S = \{1, 2, 3, 4, 5, 6\}$$

Question 13

If the probability of event $$A is$$ $$0.7$$, what is the probability of its complement $$A^c$$?

Accepted Answer

$$0.3$$

Question 14

A normal distribution has mean $$\mu = 50$$ and standard deviation $$\sigma = 10. $$What is the z-score for $$x = 70$$?

Accepted Answer

$$z = 2$$

Question 15

According to the Empirical Rule (68-95-99.7 Rule), what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 16

A researcher wants to estimate the proportion of voters who support a candidate. If the true proportion is $$p = 0.6$$ and the sample size is $$n = 100$$, what is the standard deviation of the sampling distribution of $$\hat{p}$$?

Accepted Answer

$$\sigma_{\hat{p}} = \sqrt{\frac{0.6 	imes 0.4}{100}}$$

Question 17

Which of the following is an example of response bias?

Accepted Answer

Survey respondents give answers they think are socially acceptable rather than truthful ones.

Question 18

A probability model assigns probabilities to all possible outcomes of a random phenomenon. Which of the following must be true?

Accepted Answer

The sum of all probabilities is 1.

Question 19

A researcher divides a population into groups based on age and then randomly selects individuals from each group. What sampling method is this?

Accepted Answer

Stratified random sampling

Question 20

Which of the following best illustrates the law of large numbers?

Accepted Answer

As the number of trials increases, the sample mean approaches the population mean.

Introductory Statistics Study Guide: Chapters 4–7

Study Guide - Practice Questions

Study Guide - Flashcards