Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical summary of a population, while a statistic is a numerical summary of a sample.

Question 2

A researcher collects the heights (in cm) of 100 randomly selected college students. Which type of variable is 'height' in this context?

Accepted Answer

Quantitative, continuous

Question 3

Which of the following is the correct formula for the sample mean $$\bar{x} of$$ $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 4

A histogram is most useful for displaying which type of data?

Accepted Answer

Quantitative data

Question 5

If the mean of a dataset is 50 and the standard deviation is 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 normal distribution is FALSE?

Accepted Answer

Most values lie more than three standard deviations from the mean.

Question 7

Suppose the probability of rain tomorrow is 0.3. What is the probability that it does NOT rain?

Accepted Answer

$$0.7$$

Question 8

Which of the following is the formula for the variance of a discrete random variable $$X$$ with possible values $$x_i$$ and probabilities $$P(x_i)$$?

Accepted Answer

$$\$$sigma^2$$ = \sum [(x_i - \mu)^2$ \cdot P(x_i)]$$

Question 9

A fair coin is flipped 5 times. What is the probability of getting exactly 3 heads? (Use the binomial formula.)

Accepted Answer

$$P = \binom{5}{3} (0.5)^3$ (0.5)^2$ = 0.3125$$

Question 10

Which of the following is NOT an assumption for using the Central Limit Theorem?

Accepted Answer

The population distribution must be normal for any sample size.

Question 11

A 95% confidence interval for a population mean is calculated as $$(45, 55). $$Which of the following is a correct interpretation?

Accepted Answer

We are 95% confident that the population mean is between 45 and 55.

Question 12

Which of the following would increase the width of a confidence interval for a population mean?

Accepted Answer

Increasing the standard deviation

Question 13

A Type I error occurs when:

Accepted Answer

We reject a true null hypothesis.

Question 14

Which of the following is the correct formula for the test statistic in a one-sample $$z-$$test for a population mean?

Accepted Answer

$$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$$

Question 15

A researcher wants to test if a new medication lowers blood pressure more than the current standard. Which is the appropriate alternative hypothesis?

Accepted Answer

$$H_1$$: \mu \u003c \$$mu_0$$

Question 16

Which of the following best describes the $$p-$$value in hypothesis testing?

Accepted Answer

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

Question 17

Which of the following is a correct formula for the correlation coefficient $$r$$ between variables $$X$$ and $$Y$$?

Accepted Answer

$$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2$ \sum (y_i - \bar{y})^2$}}$$

Question 18

A regression analysis yields the equation $$\hat{y} = 2 + 3x. $$What is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$\hat{y} = 14$$

Question 19

Which of the following is a requirement for a probability distribution of a discrete random variable?

Accepted Answer

The sum of all probabilities must equal 1.

Question 20

Which of the following scenarios best illustrates the use of inferential statistics?

Accepted Answer

Estimating the average income of all adults in a country based on a sample.

Elementary Statistics Course Syllabus Overview

스터디 가이드 - 연습 문제