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 Central Limit Theorem?

Accepted Answer

It states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.

Question 2

A researcher wants to estimate the average cholesterol level in adults in a city. Which of the following sampling methods would best ensure a representative sample?

Accepted Answer

Simple random sampling from a list of all adults in the city.

Question 3

Which formula correctly calculates the z-score for a value $$x in a $$normal distribution with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 4

A pharmaceutical company tests a new drug and finds a p-value of 0.03 when testing the null hypothesis that the drug has no effect. If the significance level is $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is evidence the drug has an effect.

Question 5

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

Accepted Answer

Standard deviation

Question 6

Suppose the probability of a patient recovering from a certain illness is 0.8. If 5 patients are treated independently, what is the probability that all 5 recover? (Assume independence.)

Accepted Answer

$$0.8^5$$

Question 7

Which of the following statements about correlation is TRUE?

Accepted Answer

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

Question 8

A 95% confidence interval for a population mean is calculated as (50, 60). Which of the following is a correct interpretation?

Accepted Answer

We are 95% confident that the population mean is between 50 and 60.

Question 9

Which formula gives the margin of error for a confidence interval for a population mean when the population standard deviation $$\sigma is $$unknown and the sample size is $$n$$?

Accepted Answer

$$E = t^* \frac{s}{\sqrt{n}}$$

Question 10

Which of the following is an example of a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 11

A hospital administrator wants to compare the average length of stay for patients in two different wards. Which statistical method is most appropriate?

Accepted Answer

Two-sample t-test

Question 12

Which formula is used to calculate the sample variance $$s^2$$ for a sample of $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ with sample mean $$\bar{x}$$?

Accepted Answer

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

Question 13

Which of the following best describes an observational study?

Accepted Answer

Researchers observe subjects without influencing them and record data.

Question 14

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 15

A fair coin is flipped 10 times. What is the probability of getting exactly 6 heads? (Use the binomial probability formula.)

Accepted Answer

$$P = \binom{10}{6} (0.5)^6$ (0.5)^4$

Question 16

Which of the following is a correct interpretation of a p-value?

Accepted Answer

The probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true.

Question 17

Which of the following is NOT a requirement for a binomial experiment?

Accepted Answer

The probability of success changes from trial to trial.

Question 18

A scatter plot of two variables shows a strong upward trend. Which of the following is most likely true?

Accepted Answer

The correlation coefficient is close to 1.

Question 19

Which formula is used to calculate the expected value $$E(X) of a $$discrete random variable $$X$$ with possible values $$x_1$$, $$x_2$$, ..., x_n$$ and probabilities P$$($$x_1$$), P($$x_2$$), ..., P(x_n)$$?

Accepted Answer

$$E(X) = \sum_{i=1}^n x_i P(x_i)$$

Question 20

A researcher wants to test whether a die is fair. Which statistical test should be used?

Accepted Answer

Chi-square goodness of fit test

Introduction to Statistics – Course Syllabus and Study Guide

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