Question

Perform a chi-square independence test using the critical value approach, provided the conditions for using the test are met. Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to obtain the critical value, to compute the value of the test statistic, and to state your conclusion. 160 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. At the 0.10 significance level, do the data provide sufficient evidence to support the claim that an association exists between response and major-Response and Major are dependent? Test for Independence-Contingency Tables-Chi-Square One Right Tail Test Upload Choose a File Next

this is the table given

Answer 1

We first compute the expected frequency for each of the 4 cells here as:
E_i = (Sum of row i)*(Sum of column i) / Grand Total

Also the chi square test statistic contribution for each cell is computed here as:

$\chi^2_i = \frac{(O_i - E_i)^2}{E_i}$

These computations are as shown:

Math English Correct 27 (35.00) (1.83] 43 (35.00) (1.83] Incorrect 53 (45.00) [1.42] 37 (45.00) [1.42]

The circular brackets here contains the expected frequencies for each cell, while the square bracket contains the chi square test statistic contribution here.

The chi square test statistic for this test is computed here as:

$\chi^2 = \sum \chi^2_i = \sum \frac{(O_i - E_i)^2}{E_i} = 6.5016$

Degrees of freedom here is computed as:
Df = (num of column - 1)(num of rows - 1) = 1

Therefore for 0.1 level of significance, we have from chi square distribution tables here:

$P(\chi^2_1 > 2.7055) = 0.1$

Therefore 2.7055 is the critical value for the test here.

As the test statistic value here is 6.5016 > 2.7055, which is the critical value, therefore the test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here that an association exist between response and major here.