Question 1

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

Accepted Answer

A population includes all individuals of interest, while a sample is a subset of the population.

Question 2

A pharmaceutical company wants to test a new drug. They randomly assign 100 patients to receive the drug and 100 to receive a placebo, without telling either group which they receive. What type of study is this?

Accepted Answer

Double-blind experiment

Question 3

Which of the following is a measure of central tendency?

Accepted Answer

Mean

Question 4

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

Accepted Answer

$$4$$

Question 5

If a data set has a mean of $$50$$ and a standard deviation of $$5$$, what is the $$z-$$score for a value of $$60$$?

Accepted Answer

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

Question 6

Which of the following statements about the Central Limit Theorem is correct?

Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

Question 7

A fair coin is flipped three times. What is the probability of getting exactly two heads?

Accepted Answer

$$P = \frac{3}{8}$$

Question 8

Which formula is used to calculate the sample variance $$s^2$$ for a data set with $$n$$ values and mean $$\overline{x}$$?

Accepted Answer

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

Question 9

A normal distribution has mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What is the probability that a randomly selected value is greater than $$115$$?

Accepted Answer

About $$0.16$$

Question 10

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

Accepted Answer

The probability of success changes from trial to trial.

Question 11

A researcher wants to estimate the proportion of college students who own a car. Which formula should be used to calculate the margin of error for a $$95\%$$ confidence interval for a proportion?

Accepted Answer

$$E = z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 12

Which of the following best describes the relationship between correlation and causation?

Accepted Answer

Correlation does not imply causation, but causation implies correlation.

Question 13

A scatterplot shows a strong positive linear relationship between two variables. Which value is most likely for the correlation coefficient $$r$$?

Accepted Answer

$$r = 0.9$$

Question 14

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

Accepted Answer

The number of cars passing through an intersection in an hour

Question 15

If the $$p-$$value in a hypothesis test is $$0.03$$ and the significance level $$\alpha is$$ $$0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 16

Which formula is used to calculate the least-squares regression line for predicting $$y$$ from $$x$$?

Accepted Answer

$$y = a + bx$$

Question 17

A study finds a correlation coefficient $$r = 0.05$$ between two variables. What does this indicate?

Accepted Answer

There is a weak or no linear relationship.

Question 18

Which of the following is a source of bias in sampling?

Accepted Answer

Convenience sampling

Question 19

A researcher collects data on the number of hours students study per week and their exam scores. Which variable is the explanatory variable?

Accepted Answer

Number of hours studied

Math 181-202: Elementary Statistics – Syllabus and Study Guide

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