Statistics Bingo

I just wrapped up another round of teaching stats. I co-teach two courses per year as an adjunct instructor: one class that covers intro stats and the other that hits higher level concepts. Both courses move at a high pace; they’re intended to be a survey course for professionals with a STEM background. Some students have a math background, but have never taken a statistics course. Other students have had statistics a long time ago in their undergraduate studies, but want to brush up on the material.

In both classes, by the time we get to the end, the students appreciate a light hearted activity. I found bingo to be the perfect activity to reveiw material and have a little fun. Jenny Bryan and Dean Attali have an R Shiny app for creating such bingo games. Their site has a handful of pre-populated game themes such as “boring meeting” and “bad data”. Or you can choose to create your own by pasting a list of words.

I created my own bingo questions that I ask during the game and answers that are written on the bingo cards. (Tip: Don’t forget to bring the associated list of questions to class like I did!) I’ve pasted the questions and answers below that I used for each class.

Lastly, don’t forget the sugar! M&M’s make great bingo chips. And, cookies decorated with statistics are a crowd-pleaser.

Bingo Questions for Probability & Statistics I

Questions	Answers
1. The R function used to find the area under the normal curve	pnorm
2. For a discrete random variable: $E(X)=\sum _i^n{X}_i$ * ____	$P(X)$
3. Square root of the variance	standard deviation
4. Mathematical function used to count number of possibilities: without replacement, order doesn’t matter.	choose
5. To obtain a ___ sample: Divide the population into at least two different sub-populations based on some characteristic of interest. A sample is drawn from each sub-population.	stratified
6. The Central Limit Theorem says that the distribution of the mean converges to this distribution as $n$ goes to infinity (variance must be defined).	normal
7. The ____ distribution approximates the Binomial when $n$ is large and $p$ is small. In this case we set the parameter $\lambda =np$.	Poisson
8. $P(A\cup B)=P(A)+P(B)-$ ___ ?	$P(A\cap B)$
9. Discrete distribution that models the number of successes in $n$ Bernoulli trials, where $p$ is the probability of success.	Binomial
10. The test statistic in the Test of Independence and The Goodness of Fit has a ___ distribution.	Chi-Square
11. This distribution has PMF $P(X=k)=p^k(1-p{)}^{1-k}$	Bernoulli
12. Used to control the type I error of a hypothesis test	significance level ($\alpha$)
13. In hypothesis testing, we reject the null hypothesis if the test statistic falls in the ____ region.	critical
14. Bayes Rule: $P(A|B)=$ ____ * $\frac{P(A)}{P(B)}$	$P(B|A)$
15. The area under the entire PDF curve	1
16. The continuous distribution that looks like a bell curve (except that it has fat tails), converges to normal as $n$ increases, and is used when modeling data with small sample size.	Student’s $t$
17. The maximum minus the minimum	range
18. The most frequent observation in a data sample	mode
19. The function $F(X)=P(X\le x)$.	CDF
20. A ___ provides a range for which we are $(1-\alpha )$% confident contains the true value of the population parameter. In class we considered such ranges for the true mean, $\mu$, and for proportions.	confidence interval
21. The ___ error occurs when the null hypothesis is true, but we reject it in favor of the alternative hypothesis.	Type I
22. The ___ of a hypothesis test is the probability that we reject the null hypothesis when it is in fact false.	power
23. $1-P(A)=$ the probability of the ___ of $A$.	compliment

Bingo Questions for Probability & Statistics II

Questions	Answers
1. Let {$X_i$} for $i=1..n$ partition the sample space. Bayes rule says that $f(X_i|Y)=\frac{f(Y|X_i)f(X_i)}{\sum _{i=1}^{n}f(Y|X_i)f(X_i)}$. The ___ law is used in denominator when the marginal, $f(Y)$, is unknown.	Law of Total Probability
2. Maximization of the log likelihood function (take derivative and set equal to 0)	MLE
3. Joint probability density function for two or more variables	Joint PDF
4. Result of integrating $f(X,Y)$ with respect to $Y$, over the support of $Y$	marginal of $X$
5. An alternative to frequentist statistical analysis	Bayesian statistics
6. $P(A\cap B)=P(A|B)$ * ____	$P(B)$
7. Discrete distribution that models number of trials until 1 success	Geometric (special case of negative binomial)
8. Continuous distribution use to model time until events occur	Gamma
9. True or false: $Cov(X,Y)=0$ implies $X$ and $Y$ are independent.	FALSE (TRUE if $X$ and $Y$ are jointly normally distributed. Independence implies $cov=0$ ).
10. $E(XY)=E(X)E(Y)$ when X and Y are independent	TRUE
11. $Var(X)=E(X^2)-$ ____	$E(X{)}^2$
12. $V(aX+b)=$ ___	$a^{2}V(X)$
13. Name of this function: $E(X^{tx})$ (Note: obtain $k^{th}$ moment by taking $k^{th}$ derivative and evaluating at $t$=0)	Moment Generating Function
14. Used in sampling from strata to ensure that the proportion of observations in the sample mimic the population proportions.	Proportional allocation
15. Used to control the type I error of a hypothesis test	Significance level ($\alpha$)
16. In Bayesian statistics, the population parameters are considered to be ____.	random variables
17. $P(A|B)=$ ____ * $\frac{P(A)}{P(B)}$	$P(B|A)$
18. The result of taking the derivative of the CDF with respect to the random variable (for a single random variable)	PDF
19. The second non-central moment	Variance
20. If $E(\hat{\theta })=\theta$ we say $\hat{\theta }$ is ___.	Unbiased