Answer to Question #179978 in Statistics and Probability for Vincent D'Epiro

Question

A random sample of 337 college students was asked whether or not they were registered to vote. We wonder if there is an association between a student's sex and whether the student is registered to vote. The data are provided in the tables below (expected counts are in parentheses). (All the conditions are satisfied — don't worry about checking them.)

Men Women Total

Registered 104 (102) 147 (149) 251

Not Registered 33 (35) 53 (51) 86

Total 137 200 337

A) write appropriate hypothesis

B) suppose the expected values had not been given. show how to calculate the expected number of men who are registered to vote

C)show how to calculate the component of chi² for the first cell

D) how many degrees of freedom are there?

E)find the P-value for this test

F)state your complete conclusion in context.

Answer 1

(A) $H_o$ : A student sex is independent whether the student has registered for vote.

$H_a$ : A student sex is not independent whether the student has registered for vote.

(B) So expected value od man who are registered = Probability of registered man $\times$ Total number of registered man

$=P(\text{ man registered})\times \text{Total registered man}$

$=\dfrac{104}{137}\times 104$

$=78.94$

(C) $\chi^2 value=\sum \dfrac{(O-E)^2}{E}$

$=\sum [\dfrac{(104-102)^2}{102},\dfrac{(35-33)^2}{33}]=\sum[0.0392,0.1212]=0.1604$

(D) Th degree of freedom here is 2.

(E) p-value for the above test is 0.202

(F) We do not have proper evidence to suggest that there is a significant association/ dependence between sex and voter status.