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

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

Question 1

Which of the following best describes the difference between a population and a sample in statistics?

Accepted Answer

A population is the entire group of interest, while a sample is a subset selected from that population.

Question 2

A pharmaceutical company wants to estimate the average recovery time for a new drug. They randomly select 100 patients from a hospital and record their recovery times. Which term best describes the 100 patients?

Accepted Answer

Sample

Question 3

Which of the following is the correct formula for the mean of a data set with $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 4

A researcher collects the following data on the number of hours students study per week: 5, 7, 8, 10, 10, 12, 15. What is the median?

Accepted Answer

10

Question 5

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

Accepted Answer

Range

Question 6

If the standard deviation of a data set is 0, what does this imply about the data?

Accepted Answer

All values are equal.

Question 7

Which formula is used to calculate the variance of a sample with $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$ and sample mean $$\bar{x}$$?

Accepted Answer

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

Question 8

A medical study finds that the correlation coefficient between hours of exercise per week and cholesterol level is $$r = -0.65. $$What does this indicate?

Accepted Answer

There is a strong negative linear relationship.

Question 9

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

Accepted Answer

$$\frac{1}{3}$$

Question 10

Which of the following best describes a normal distribution?

Accepted Answer

A distribution where the mean, median, and mode are all equal.

Question 11

A hospital records the blood pressure of 200 patients. The data is grouped into intervals. Which type of graph is most appropriate to display this data?

Accepted Answer

Histogram

Question 12

A student scores 85 on a test where the mean is 80 and the standard deviation is 5. What is the student's z-score?

Accepted Answer

$$z = \frac{85 - 80}{5} = 1$$

Question 13

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

Accepted Answer

The number of cars passing through a toll booth in an hour.

Question 14

A survey asks respondents to rate their satisfaction on a scale from 1 to 5. What level of measurement is this?

Accepted Answer

Ordinal

Question 15

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 16

A researcher wants to test if a new teaching method improves test scores. Which statistical test is most appropriate?

Accepted Answer

Hypothesis test for the mean

Question 17

Which formula is used to calculate the confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

$$\bar{x} \pm t_{\alpha/2} \frac{s}{\sqrt{n}}$$

Question 18

A company claims their light bulbs last an average of 1200 hours. A sample of 30 bulbs has a mean of 1180 hours and a standard deviation of 50 hours. What is the test statistic for a one-sample t-test?

Accepted Answer

$$t = \frac{1180 - 1200}{50 / \sqrt{30}}$$

Question 19

Which of the following best describes the purpose of a regression analysis?

Accepted Answer

To predict the value of one variable based on another.

Question 20

A school wants to know if there is an association between students' favorite subject (Math, Science, English) and their grade level (Freshman, Sophomore, Junior, Senior). Which statistical test should be used?

Accepted Answer

Chi-square test for independence

MAT152 Introductory Statistics: Course Schedule and Chapter Overview

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