# Multiple Sample Hypothesis Testing with Playing Cards

Q1

Multiple Sample Hypothesis Testing with Playing Cards

• Take a standard deck of 52 playing cards.  Separate the cards into 4 stacks by suit.  For our purposes, let’s assume the Ace is worth 1 point, 2 through 10 are worth their respective points, Jack is worth 11 points, Queen is worth 12 points, and King is worth 13 points.  So there are 4 suits with values of 1 through 13 in them.  The average value of all cards is 7.00.
• From the Diamonds, remove the A, 2, 3 and 4; shuffle the rest of the stack and randomly choose 4 cards.
• From the Hearts, remove the A, 2, Q and K; shuffle the rest of the stack and randomly choose 4 cards.
• From the Clubs, remove the 10, J, Q and K; shuffle the rest of the stack and randomly choose 4 cards.
• From the Spades, remove nothing; shuffle the entire stack and randomly choose 4 cards.
• Using the Excel file for Analysis of Variance, conduct an ANOVA to test for a difference in the means for the four suits.  Use a .05 significance level.  If the null is rejected, be sure to look at the post hoc test results that follow.
• After each student has posted their results, which will include the card values for each suit and the p-value, conclusion and post hoc results for the hypothesis test, the instructor will summarize the findings.  What we should see is that many samples will probably show a significant  difference between the suits since the values are lower for some suits and higher for others.

Q2

Many alleged studies are misleading in that the conclusions are often based on undisclosed premises.  Parenting books state that an advantage to breastfeeding is that it makes women healthier; what is not stated is that women who breastfeed tend to follow stricter diets, and it is the diets that actually makes them healthier.  If you looked at statistics for the number of tires replaced in a given year, would you be surprised to find out that Toyota Camry tops the list for wearing out tires?  It shouldn’t since it is the most popular car in America.  And in 2000, Sen. Daschle (D-South Dakota) pushed his gun control agenda against Pres. Bush when he stated “Do you realize that the majority of vendors at gun shows don’t do background checks on their customers;” while true, what he failed to mention is that the majority of vendors at gun shows don’t sell guns (they sell food, t-shirts, souvenirs, etc.), but not guns.

Nonetheless, this quasi-truth aroused the voters.  Name another conclusion that, while true, is based on misconception.  There are multitudes of them in regards to health and politics, so keep your eyes open.  If you cannot find one, then make one up (use your creativity and silliness if you wish).

q3

Infomercials often peddle products under the guise of “studies show…”.  While some of the products are surprisingly good (e.g., FoodSaver, Foreman Grill, Ronco Rotisserie), many of the products are not.  Why should you be initially suspicious of any products advertised on these shows, despite the “existence” of data? What factors would help to convince you that the claims might be true?

q4

The plain M&M’s Milk Chocolates are mass-produced with a distribution of 24% blue, 20% orange, 16% green, 14% yellow, 13% red and 13% brown.  The peanut M&M’s are mass-produced with a distribution of 23% blue, 23% orange, 15% green, 15% yellow, 12% red and 12% brown.

• Open a packet of your favorite M&Ms, plain or peanut.
• Count the number of M&M’s in the packet.
• Count number of BLUE, ORANGE, GREEN, YELLOW, RED and BROWN candies.
• Using the Excel file for Chi Square Testing, conduct a Goodness of Fit test to determine if the distribution of colors in the package fits the expected distribution.  Use a .05 significance level.  Be sure to use the percentages shown above as the expected values.
• After each student has posted their results (including the totals for each color and the p-value and conclusion for the hypothesis test, the instructor will summarize the findings.  What we should see is that most, if not all, of the packages will fit the expected distribution, but with a small package of candy, anything is possible

Q5

Regression and Correlation are the most used and most abused tools in research.  People are quick to jump to conclusions that if a relationship exists between two variables, then one must cause the other.  There are many reasons why two variables can be related without causality.  For example, there is a strong inverse relationship between the sale of ice cream and the number of reported cases of the flu — does ice cream cure the flu?  Of course not, but more ice cream is consumed in the summer, when the flu is minimized, thus there is a seasonal relationship, not a causal one.  There is also a relationship between the seat belt lights turning on in an airplane and the existence of turbulence in flight, but the lights do not cause the turbulence.

Give a plausible explanation for the following correlations:

• 1) There is a strong relationship between the amount of money people spend and the amount people save (in other words, people who spend more tend to save more).  Does this mean that you can improve your life savings by spending more money?  Explain how this correlation is true.
• 2) There is a strong relationship between the number of cops on our streets and the number of reported crimes.  Does this mean that cops commit crimes or that criminals are more bold when cops are on the streets?  Explain how this correlation is true.

q6

Name a situation in which a relationship exists in which people tend to jump to false conclusions about one variable causing the other.  There are many out there, so think hard.

Q7

For today’s experiment, no candy or cards are needed.  You just need to use what you already know (or you can take an educated guess).

• Think of at least 10 married couples you know.Write down their names.For each couple, write down the husband’s age followed by his wife’s age.If you are not sure, you can ask them or just take an educated guess.
• As long as you have at least 10 couples, you can proceed with the analysis; otherwise, keep thinking (and it could be people you just see at church or running the local store — you don’t have to know them well).
• Using the Excel file for Correlation Analysis, conduct a Correlation test to determine if there is a correlation between a husband’s age and his wife’s age.Use a .05 significance level.Be sure to put the husband’s age in the left column (the Independent Variable) and the wife’s age in the right column (the Dependent Variable).
• Is the correlation significant?What is the correlation coefficient?What is the regression equation that predicts the wife’s age from the husband’s age?
• After each student has posted their results (including the ages, p-value, correlation coefficient, and regression equation) the instructor will summarize the findings and combine the data to create a new correlation coefficient and regression equation.