Q: A student receives grades of 80, 85, and 90 in three courses, weighted by credits 2, 3, and 5 respectively. What is the weighted mean?

$$\frac{80 \times 2 + 85 \times 3 + 90 \times 5}{2 + 3 + 5} = 87$$

Q: If two events A and B are independent, which formula gives the probability that both occur?

$$P(A \text{ and } B) = P(A) \times P(B)$$

Q: If the probability of event A is $$0.4$$ and the probability of event B is $$0.5$$, and they are not disjoint, what is the probability that A or B occurs?

$$0.4 + 0.5 - P(A \text{ and } B)$$

Question 1

Which of the following levels of measurement allows for meaningful calculation of ratios, such as doubling or halving values?

Accepted Answer

Ratio

Question 2

A researcher selects every 10th person from a list of 1,000 registered voters. Which sampling method is being used?

Accepted Answer

Systematic sampling

Question 3

A medical study follows a group of patients over 10 years to observe the development of heart disease. What type of observational study is this?

Accepted Answer

Prospective

Question 4

Given a frequency distribution with class limits 10–19, 20–29, 30–39, what is the class width?

Accepted Answer

$$10$$

Question 5

Which of the following is NOT a characteristic of a normal distribution?

Accepted Answer

The tails of the distribution touch the horizontal axis

Question 6

A time-series graph is most appropriate for displaying:

Accepted Answer

Changes in a variable over time

Question 7

If a dataset contains an extreme outlier, which measure of center is most likely to be affected?

Accepted Answer

Mean

Question 8

A student receives grades of 80, 85, and 90 in three courses, weighted by credits 2, 3, and 5 respectively. What is the weighted mean?

Accepted Answer

$$\frac{80 	imes 2 + 85 	imes 3 + 90 	imes 5}{2 + 3 + 5} = 87$$

Question 9

According to the range rule of thumb, what is the approximate standard deviation for a dataset with a maximum value of 50 and a minimum value of 10?

Accepted Answer

$$\frac{50 - 10}{4} = 10$$

Question 10

If two events A and B are independent, which formula gives the probability that both occur?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Question 11

A fair six-sided die is rolled. What is the probability of rolling a number less than 5?

Accepted Answer

$$\frac{4}{6}$$

Question 12

Which of the following best describes a sampling distribution?

Accepted Answer

The distribution of a statistic over all possible samples from a population

Question 13

When is it appropriate to use the normal distribution to approximate the sampling distribution of the sample mean?

Accepted Answer

When the sample size is large ($$n \geq 30) or $$the population is normal

Question 14

A 95% confidence interval for a population mean is calculated as $$[50, 60]. $$Which interpretation is correct?

Accepted Answer

We are 95% confident that the population mean is between 50 and 60

Question 15

Which scenario describes a Type I error?

Accepted Answer

Rejecting a true null hypothesis

Question 16

A p-value is calculated as $$0.03$$ for a hypothesis test with $$\alpha = 0.05. $$What is the correct conclusion?

Accepted Answer

Reject the null hypothesis

Question 17

If the probability of event A is $$0.4$$ and the probability of event B is $$0.5$$, and they are not disjoint, what is the probability that A or B occurs?

Accepted Answer

$$0.4 + 0.5 - P(A 	ext{ and } B)$$

Question 18

A z-score is calculated as $$z = \frac{x - \mu}{\sigma}. If$$ $$x = 70$$, $$\mu = 60$$, and $$\sigma = 5$$, what is the z-score?

Accepted Answer

$$z = 2$$

Question 19

A researcher wants to test whether the mean blood pressure in a population is different from 120 mmHg. Which type of hypothesis test should be used?

Accepted Answer

A test for population mean

Introductory Statistics Exam 1 Study Guide: Key Concepts and Methods

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