Q: Which formula represents the covariance between two variables $X$ and $Y$?

$\text{Cov}(X, Y) = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})$

Q: A casino game pays $\$10$ for a win and $\$0$ for a loss. The probability of winning is $0.2$. What is the expected payout per game?

$E[X] = 10 \times 0.2 + 0 \times 0.8 = 2$

Question 1

Which of the following best describes the concept of 'regression to the mean' as discussed in the course?

Accepted Answer

It is the tendency for extreme values in a dataset to be followed by values that are closer to the average.

Question 2

A company wants to compare the average SAT scores of its employees to the national average. Which measure of central tendency should they use to summarize their employees' SAT scores?

Accepted Answer

Mean

Question 3

If the standard deviation of a dataset is high, what does this indicate about the data?

Accepted Answer

The data points are spread out widely from the mean.

Question 4

Given a dataset with values $x_1, x_2, ..., x_n$, which formula correctly calculates the sample variance?

Accepted Answer

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

Question 5

A business analyst calculates the z-score for an employee's sales performance as $z = 2.5$. What does this indicate?

Accepted Answer

The employee's sales are 2.5 standard deviations above the mean.

Question 6

Which formula represents the covariance between two variables $X$ and $Y$?

Accepted Answer

$	ext{Cov}(X, Y) = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})$

Question 7

A medical test for a disease has a sensitivity of 90% and a specificity of 80%. If the disease prevalence is 5%, what statistical concept should be used to calculate the probability that a person who tests positive actually has the disease?

Accepted Answer

Bayes Rule

Question 8

Which formula gives the expected value of a discrete random variable $X$ with possible values $x_1, x_2, ..., x_n$ and probabilities $p_1, p_2, ..., p_n$?

Accepted Answer

$E[X] = \sum_{i=1}^{n} x_i p_i$

Question 9

A casino game pays $\$10$ for a win and $\$0$ for a loss. The probability of winning is $0.2$. What is the expected payout per game?

Accepted Answer

$E[X] = 10 	imes 0.2 + 0 	imes 0.8 = 2$

Question 10

Which formula represents the probability of exactly $k$ successes in $n$ independent Bernoulli trials with probability $p$ of success?

Accepted Answer

$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$

Question 11

A pollster wants to estimate the proportion of voters who support a candidate. Which formula should be used to calculate the standard error of the sample proportion $\hat{p}$?

Accepted Answer

$SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

Question 12

According to the Central Limit Theorem, what happens to the distribution of sample means as the sample size increases?

Accepted Answer

It approaches a normal distribution, regardless of the population distribution.

Question 13

A company wants to test if a new marketing campaign increases sales. Which statistical method should they use to compare the mean sales before and after the campaign?

Accepted Answer

Hypothesis Testing

Question 14

Which formula gives the confidence interval for the mean $\mu$ of a normal distribution with known variance $\sigma^2$ and sample size $n$?

Accepted Answer

$\bar{x} \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

Question 15

A soda company wants to test if the variance in soda volume is different from the advertised value. Which distribution should be used for hypothesis testing about variance?

Accepted Answer

Chi-squared ($\chi^2$) distribution

Question 16

In linear regression, what does the $R^2$ statistic represent?

Accepted Answer

The proportion of variance in the dependent variable explained by the independent variables.

Question 17

A business wants to model viral growth in sales using a non-linear regression. Which functional form is most appropriate for modeling exponential growth?

Accepted Answer

$y = a e^{bx}$

Question 18

A researcher includes a dummy variable for gender in a regression model. What does the coefficient on the dummy variable represent?

Accepted Answer

The difference in the conditional mean of the dependent variable between genders.

Question 19

Which formula represents the least squares estimate of the slope $\beta_1$ in a simple linear regression of $y$ on $x$?

Accepted Answer

$\beta_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$

EC 1151.02: Statistics – Syllabus and Course Structure Overview

Study Guide - Practice Questions

Study Guide - Flashcards