Question

3. We would like to find out, whether the voting preference of the population depend on the age or not. A poll was conducted among 600 citizens, collecting their age and political preferences (2 RU Liberal Conservative Other 18-30 49 43 28 120 31-45 71 61 18 150 46-65 68 79 13 160 >65 91 54 25 170 279 237 84 600 a) What are the hypotheses? H: Ha b) Calculate the test statistic and p-value 18-30 31-45 46-65 >65 Liberal Conservative Other

Answer 1

The Observed frequency ware:

	18-30	31-45	46-65	>65
Liberl	49	71	68	91	279
Conservative	43	61	79	54	237
Other	28	18	13	25	84
	120	150	160	170	600

The Hypotheses are :

$\H_0$_{$H_0$ : The voting preference of the population independent of the age}

_{$H_1$ :   The voting preference of the population not independent of the age}

_{Hence, we calculate the expected frequencies in each category by multiplying the row and column totals and dividing by 600 :}

	18-30	31-45	46-65	>65
Liberl	55.8	69.75	74.4	79.05	279
Conservative	47.4	59.25	63.2	67.15	237
Other	16.8	21	22.4	23.8	84
	120	150	160	170	600

So, We can now calculate the value of Chi- square statistics

$\sum_{i=1}^{4}{}(O_i - E_i)^2 / E_i}$  

= (49-55.8)^2/55.8 + ......... +(25.23.8)^2/23.8   

== 0.8287 + 0.0224+ 0.5505+ 1.806 + 0.4084 + 0.05168 + 3.92 + 2.575 +7.467 +0.4285 +3.945 +0.0605

=== 22.063

Now, the no. of degree of freedom is (3-1)(4-1) == 6

Test statistics === 22.063

We are carring out one side test . Our observed value of Test statistics exceeds 18.55 , the upper 0.5% point of chi sq . distribution of 6 degree of freedom .

So we have sufficent evidence to reject   $H_0$ at the 0.5% level .

Therefore , the reasonable conclude that the   ^,

^{The voting preference of the population dependent of the age.}  

The p value is given by

p($X^2$ > 22.06)

1-  p($X^2$ < 22.06) == 0.0012