Chi Square Quiz

1) The spinner in a board game has eight colors the arrow can land on. To test
the fairness of the spinner, you spin the arrow 75 times and get the following results:

Green: 3 Blue: 13 Red: 9 Orange: 9
Brown: 16 Yellow: 14 White: 8 Black: 3

Calculate the chi-square statistic for this data and use the table to find the p-value.

2) Your friend says she has an unfair die: The probability of getting a one or six
is 1/3 for each, and the probability of getting a two, three, four, or five is 1/12 each.
If you roll this dice 96 times, what are the expected values for each number of the die?

a) The expected values of 8 for both ones and sixes, and 32 for twos, threes, fours, and fives.
b) The expected values are 32 for both ones and sixes, and 8 for twos, threes, fours, and fives.
c) All categories have the same expected value of 16
d) All categories have the same expected value of 32
e) The expected values are 8 for ones, twos, threes, and 32 for fours, fives and sixes

3) Criminologists have long debated whether there is a relationship between weather and violent crime.
the author of the article "Is there a Season for Homicide?"(Criminology 1998): 287-296) classified
1361 homicides according to season, resulting in the accomanying data. Does this data support the
theory that the homicide rate is not the same over the four seasons? Test the relevant hypothesis using
a significance level of 0.05.

Winter Spring Summer Fall
328 334 372 327

4. Titanic Below is a table that shows who survived the sinking of the Titanic based on whether
they were crewmembers, or passengers booked in first-, second-, or third-class staterooms.

Crew First Second Third Total
Alive 212 202 118 178 710
Dead 673 123 167 528 1491
Total 885 325 285 706 2201

a) If we draw an individual at rondom from this table, what is the probability that we will draw a member of the crew?
b) What is the probability of randomly selecting a third class passenger who survived?
c) What is the probability of a randomly selected passenger surviving, given that the passenger was a first class passenger?
d) If someone's chances of surviving were the same regardless of their status on the ship, how many members fo the crew would you expect to have lived?
e) State the null and alternative hypothesis?
f) What is the degree of freedom for this test?
g) Calculate the chi-square value and interpret the results?

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