Question

6. Using the ChrSquare test to determine whether dass in college is independent of favorite type of movie, glven data: Comedy Sci-Fi 13 90 65 14th 75 90 15th 80 75 16 65 80 a) Find the expected values. (put next to Observed) b) Find the test statistic.

Answer 1

Chi-square test for indipendence is to be used here.

Then the null and alternate hypothesis will be,

H_o: There is no association between the two variables (class in college and type of movie), i.e, they are indipendent.

H₁:There is an association between the two variables (class in college and type of movie), i.e, they are dependent.

a) The expected values (E) are calculated using the formula,  

$E=\left ( RowTotal \right*ColumnTotal )/GrandTotal$

I will put observed and expected values in one table with the expected values inside parantheses.

	Comedy	Sci-fi	Total
13th	90 (77.5)	65 (77.5)	155
14th	75 (82..5)	90 (82.5)	165
15th	80 (77.5)	75 (77.5)	155
16th	65 (72.5)	80 (72.5)	145
Total	310	310	620

Both observed and expected values are given in the table with expected values written inside parantheses. The bold value indicates the grand total.

b)  The test statistic is given by,

  $\chi ^{2}= \sum_{i} \left ( O_{i} \right - E_{i})^{2}/ E_{i}$

O_i denotes the observed values and E_i denotes the expected values. The value of the test staistic will be obtained after directly substituting the values in the equation. Then,

$\chi ^{2}$=7.106

correct to three decimal points.