Q: If two events A and B are independent, which equation must be true?

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

Question 1

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

Accepted Answer

A population parameter describes a characteristic of the entire population, while a sample statistic describes a characteristic of a sample.

Question 2

A researcher collects the heights (in cm) of 100 randomly selected college students and finds the mean to be 170 cm with a standard deviation of 10 cm. Which formula would you use to calculate the z-score for a student who is 185 cm tall?

Accepted Answer

$$z = \frac{185 - 170}{10}$$

Question 3

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Question 4

A histogram is used to:

Accepted Answer

Display the frequency distribution of quantitative data

Question 5

If the probability of rain tomorrow is 0.3, what is the probability that it will NOT rain?

Accepted Answer

$$1 - 0.3 = 0.7$$

Question 6

Which of the following scenarios best illustrates the use of the Central Limit Theorem?

Accepted Answer

Estimating the mean height of all adults in a city by taking the means of many random samples

Question 7

A company claims that at least 90% of its products pass quality control. You take a random sample of 100 products and find that 85 pass. Which hypothesis test would you use to evaluate the company's claim?

Accepted Answer

A hypothesis test for a population proportion

Question 8

Which formula would you use to calculate the variance of a sample?

Accepted Answer

$$s^2$$ = \frac{\sum (x_i - \overline{x}$$)^2$$}{n-1}$$

Question 9

Which of the following is an example of a discrete random variable?

Accepted Answer

The number of cars passing through an intersection in an hour

Question 10

A researcher wants to estimate the average cholesterol level of adults in a city. Which formula should be used to construct a 95% confidence interval for the population mean when the population standard deviation is unknown?

Accepted Answer

$$\overline{x} \pm t^* \frac{s}{\sqrt{n}}$$

Question 11

Which of the following statements about correlation is TRUE?

Accepted Answer

A correlation coefficient close to 1 indicates a strong positive linear relationship.

Question 12

If two events A and B are independent, which equation must be true?

Accepted Answer

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

Question 13

A medical test for a disease has a 95% probability of correctly identifying a diseased patient (true positive rate). If 100 patients with the disease are tested, what is the expected number of true positives?

Accepted Answer

$$100 	imes 0.95 = 95$$

Question 14

Which of the following is the correct formula for the regression line used to predict y from x?

Accepted Answer

$$y = b_0$ + b_1$ x$$

Question 15

A sample of 50 students has a mean test score of 80 with a standard deviation of 8. What is the standard error of the mean?

Accepted Answer

$$\frac{8}{\sqrt{50}}$$

Question 16

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis

Question 17

A study finds a p-value of 0.03 when testing a hypothesis at the 0.05 significance level. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis

Question 18

Which of the following is NOT a requirement for using the binomial probability formula?

Accepted Answer

The probability of success changes from trial to trial

Question 19

A researcher wants to compare the mean blood pressure between two independent groups. Which statistical test should be used?

Accepted Answer

A two-sample t-test

Question 20

Which of the following best describes the purpose of using a stem-and-leaf plot?

Accepted Answer

To display the distribution of a data set while preserving the original data values

STA2023 Introductory Statistics Syllabus & Study Guide

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