A recent news report indicated that out of 75 people polled,35 men and 10 women had given the president a high approval rating,while 20 men and 10 women had given the president a low approval rating.Using a two-way test for independence,what is ?
A)3.00
B)3.33
C)3.58
D)3.72

Question

A recent news report indicated that out of 75 people polled,35 men and 10 women had given the president a high approval rating,while 20 men and 10 women had given the president a low approval rating.Using a two-way  test for independence,what is  ?
A)3.00 
B)3.33 
C)3.58 
D)3.72

Quizplus · Accepted Answer

To find out whether there is a significant relationship between gender and approval rating, we need to carry out a chi-squared test for independence.

First, we construct a contingency table:

High rating   Low rating   Total
Men:      35            20           55
Women:    10            10           20
Total:    45            30           75

The observed (O) and expected (E) frequencies for each cell are:

High rating   Low rating  
Men:      O = 35        O = 20       E = (55*45)/75 = 33
Women:    O = 10        O = 10       E = (20*45)/75 = 12
          
To calculate the chi-squared statistic, we use the formula:

chi-squared = sum((O - E)^2 / E)

Plugging in the values, we get:

chi-squared = ((35-33)^2 / 33) + ((20-33)^2 / 33) + ((10-12)^2 / 12) + ((10-8)^2 / 12)
            = 0.424 + 3.273 + 0.333 + 0.333
            = 4.363

Using a chi-squared distribution table with 1 degree of freedom (df = (number of rows - 1) x (number of columns - 1)), we find the critical value to be 3.58 at the 5% level of significance. Since our calculated chi-squared value (4.363) is greater than the critical value (3.58), we reject the null hypothesis and conclude that there is a significant relationship between gender and approval rating.

Therefore, the answer is: C (3.58).

A Recent News Report Indicated That Out of 75 People