Question

	Play Chess	Don't Play Chess
Male Students	25	162
Female Students	19	148

Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their college. Answer the following questions about the table . Be sure to show any calculations.

a. How many students in total were surveyed?

b. How many of the students surveyed play chess?

c. What question about the population of students at the state college would this table attempt to answer/

d. State H o and H a for the test related to this table.

Answer 1

a) Total number of students surveyed is = 25+162+19+148= 354

b) Number of students surveyed play chess

=Number of male students who play chess + Number of female student who play chess

= 25 +19

= 44

c) As the 2X2 contingency table gives a sample data about gender and playing chess, it attempts to answer whether there is relationship between gender and playing chess. (whether any of the gender is more interested to play chess or not)

Note :That is whether two categorical variables gender and playing chess are dependent or independent. The test used is Chi square test of independence .

d) The null hypothesis is

H0 : There is no relationship between gender and playing chess

The alternative hypothesis is

Ha : There is a strong relationship between gender and playing chess.

Note : With the use of the given contingency table (which are observed frequencies, Oi ) , we find out expected frequencies (Ei) if gender and playing chess are independent .

Calculation of Ei

	play	don’t play	total
male	25	162	187
female	19	148	167
toatl	44	310	354

E(25) = 187*44/354 = 23.24

E(162) = 187-23.24 = 163.76

etc

Then calculate chi square test statistic

if the value of test statistic more  than critical value , we reject H0.