Q: Which formula is used to calculate the probability $$P(A \cap B) of $$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 healthcare?

Accepted Answer

To summarize and analyze information in order to make evidence-based decisions.

Question 2

A researcher wants to compare the average blood pressure between two groups: those who exercise regularly and those who do not. Which statistical test is most appropriate?

Accepted Answer

Two-sample t-test

Question 3

Which formula correctly calculates the sample mean $$\bar{x}$$ for a dataset with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 4

A hospital administrator wants to know if the proportion of patients who recover within a week differs between two treatments. Which hypothesis test should be used?

Accepted Answer

Hypothesis test for population proportions

Question 5

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

Accepted Answer

Ignoring outliers

Question 6

A survey is conducted to estimate the average number of hours college students sleep per night. Which term best describes the group of all college students in this context?

Accepted Answer

Population

Question 7

Which formula represents the variance $$s^2 of a $$sample with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ and sample mean $$\bar{x}$$?

Accepted Answer

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

Question 8

A pharmaceutical company wants to test if a new drug is more effective than the current standard. Which is the null hypothesis $$H_0 in $$this scenario?

Accepted Answer

$$H_0$$: There is no difference in effectiveness between the new drug and the current standard.

Question 9

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

Accepted Answer

Rejecting a true null hypothesis

Question 10

A student calculates the correlation coefficient $$r$$ between study hours and exam scores and finds $$r = 0.85. $$What does this indicate?

Accepted Answer

There is a strong positive linear relationship.

Question 11

Which formula is used to calculate the probability $$P(A \cap B) of $$two independent events $$A$$ and $$B$$ both occurring?

Accepted Answer

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

Question 12

A researcher uses a random sample to estimate the mean income of all residents in a city. Which term describes the mean income of all residents?

Accepted Answer

Parameter

Question 13

Which of the following is a categorical variable?

Accepted Answer

Favorite type of music

Question 14

A student wants to test if the average time spent on homework differs between freshmen and seniors. Which statistical method should be used?

Accepted Answer

Two-sample t-test

Question 15

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

Accepted Answer

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

Question 16

A teacher wants to know if there is an association between students' preferred study method (group or solo) and their final grade category (A, B, C, D, F). Which test should be used?

Accepted Answer

Chi-square test for association between categorical variables

Question 17

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize data; inferential statistics draw conclusions about populations.

Question 18

A student is analyzing the relationship between hours of sleep and test scores using regression analysis. Which equation best represents a simple linear regression model?

Accepted Answer

$$y = \$$beta_0$$ + \$$beta_1$$ x + \epsilon$$

Question 19

A coin is flipped 10 times. What is the probability of getting exactly 5 heads? (Assume a fair coin.)

Accepted Answer

$$P = \binom{10}{5} 	imes (0.5)^5$ 	imes (0.5)^5$

Question 20

A student wants to estimate the proportion of students who prefer online learning. Which formula should be used to calculate the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{x}{n}$$

Introduction to Statistics (MAT 220A-OL) – Syllabus and Study Guide

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