Q: If two events A and B are independent, which of the following is true?

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

Question 1

Which of the following best describes the difference between an observational study and a designed experiment?

Accepted Answer

A designed experiment involves manipulating variables to observe outcomes, while an observational study only observes without intervention.

Question 2

A researcher wants to study the effect of a new medication on blood pressure. She randomly assigns 100 patients to receive either the medication or a placebo and measures their blood pressure after 8 weeks. What type of study is this?

Accepted Answer

Designed experiment

Question 3

Which of the following sampling methods is most likely to produce a representative sample of a large population?

Accepted Answer

Simple random sampling

Question 4

A frequency distribution table is used to:

Accepted Answer

Summarize qualitative data by showing the number of observations in each category.

Question 5

Which graphical display is most appropriate for showing the distribution of a single quantitative variable?

Accepted Answer

Histogram

Question 6

Suppose the mean of a data set is 50 and the standard deviation is 5. What is the z-score for a value of 60?

Accepted Answer

$$z = \frac{60 - 50}{5} = 2$$

Question 7

Which measure of central tendency is most affected by extreme values (outliers)?

Accepted Answer

Mean

Question 8

A box-and-whisker plot is useful for:

Accepted Answer

Identifying the median, quartiles, and potential outliers in a data set.

Question 9

If two events A and B are independent, which of the following is true?

Accepted Answer

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

Question 10

A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

$$P = \frac{2}{6} = \frac{1}{3}$$

Question 11

Which of the following is the formula for the variance of a population?

Accepted Answer

$$\$$sigma^2$$ = \frac{\sum (x_i - \mu)^2$}{N}$$

Question 12

A researcher collects data on the number of emails received per day by employees in a company. Which probability distribution is most appropriate to model this data?

Accepted Answer

Poisson distribution

Question 13

Which of the following statements about the normal distribution is TRUE?

Accepted Answer

The mean, median, and mode are all equal.

Question 14

A 95% confidence interval for a population mean is calculated as (45, 55). What does this mean?

Accepted Answer

We are 95% confident that the population mean is between 45 and 55.

Question 15

Which of the following is the correct formula for the test statistic in a one-sample z-test for a population mean?

Accepted Answer

$$z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$$

Question 16

A scatterplot shows a strong positive linear relationship between two variables. Which of the following is most likely true about the correlation coefficient $$r$$?

Accepted Answer

$$r is $$close to 1

Question 17

Which of the following is an example of a categorical variable?

Accepted Answer

Favorite type of music

Question 18

A chi-square test for independence is used to:

Accepted Answer

Test whether two categorical variables are related.

Question 19

Which of the following best describes the purpose of exploratory data analysis (EDA)?

Accepted Answer

To summarize and visualize data to uncover patterns and insights.

Question 20

A researcher wants to estimate the proportion of voters who support a new policy. Which formula should be used to calculate the required sample size for a given confidence level and margin of error?

Accepted Answer

$$n = \left( \frac{z^*}{E} \$$right)^2$$ p(1-p)$$

Introductory Statistics (MATH 125 HK) – Syllabus and Course Structure Study Guide

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