Q: Which formula is used to calculate the probability of two independent events A and B both occurring?

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

Question 1

Which of the following best describes the primary purpose of statistics in scientific research?

Accepted Answer

To organize, analyze, and interpret data to make informed decisions.

Question 2

A pharmaceutical company wants to test the effectiveness of a new drug. Which statistical concept is most relevant for designing their experiment?

Accepted Answer

Experimental design and frequency distributions.

Question 3

Given the following data set: 2, 4, 4, 6, 8, what is the mean?

Accepted Answer

$$ \frac{2+4+4+6+8}{5} = 4.8 $$

Question 4

Which measure of central tendency is most appropriate for describing the typical value in a highly skewed distribution?

Accepted Answer

Median

Question 5

A hospital records the blood pressure of 100 patients. Which graph would best display the frequency distribution of their systolic blood pressure readings?

Accepted Answer

Histogram

Question 6

If the probability of a patient recovering from a disease is 0.8, what is the probability that two randomly selected patients both recover?

Accepted Answer

$$ 0.8 	imes 0.8 = 0.64 $$

Question 7

Which formula is used to calculate the standard deviation of a sample?

Accepted Answer

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

Question 8

A researcher wants to test if the average height of students in two different colleges is the same. Which statistical test should be used?

Accepted Answer

Hypothesis test for two population means

Question 9

Which of the following is NOT a valid assumption for using the normal distribution?

Accepted Answer

The data are categorical.

Question 10

A company wants to predict future sales based on advertising expenditure. Which statistical method is most appropriate?

Accepted Answer

Linear regression

Question 11

If a population is normally distributed with mean $$ \mu = 50 $$ and standard deviation $$ \sigma = 10 $$, what is the z-score for a value of 70?

Accepted Answer

$$ z = \frac{70 - 50}{10} = 2 $$

Question 12

Which of the following best describes the concept of 'statistical inference'?

Accepted Answer

Drawing conclusions about a population based on sample data.

Question 13

A survey finds that 60% of respondents prefer online shopping. If 5 people are randomly selected, what is the probability that exactly 3 prefer online shopping? (Use binomial probability)

Accepted Answer

$$ P(X=3) = \binom{5}{3} (0.6)^3$ (0.4)^2$ = 0.3456 $$

Question 14

Which of the following is a measure of position?

Accepted Answer

Percentile

Question 15

A researcher wants to test if the proportion of smokers in two cities is different. Which test should be used?

Accepted Answer

Hypothesis test for two population proportions

Question 16

Which formula is used to calculate the probability of two independent events A and B both occurring?

Accepted Answer

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

Question 17

Which of the following is a valid interpretation of a p-value in hypothesis testing?

Accepted Answer

The probability of observing the sample data, or something more extreme, if the null hypothesis is true.

Question 18

A student scores in the 85th percentile on a standardized test. What does this mean?

Accepted Answer

The student scored higher than 85% of the test takers.

Question 19

Which of the following is NOT a step in the process of statistical problem solving?

Accepted Answer

Ignoring outliers

Question 20

A researcher finds a correlation coefficient $$ r = 0.95 $$ between hours studied and exam scores. What does this indicate?

Accepted Answer

A strong positive linear relationship between hours studied and exam scores.

Statistics I (MATH 1200) Syllabus and Course Overview

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드