Question

A review of voter registration records in a small town yielded the following table of the number of males and females registered as Democrat, Republican, or some other affiliation.

Affiliation
Democrat
300 Male
600 Female

Republican
500 Male
300 Female

Other
200 Male
100 Female

Suppose we wish to test the null hypothesis that there is no association between party affiliation and gender. Under the null hypothesis, what is the expected number of male Democrats?

A) 300
B) 333.3
C) 450
D) 500

Answer 1

The expected number of male Democrats under the null hypothesis is 450, calculated by multiplying the row and column totals and dividing by the grand total.

Step-by-step explanation:

The expected number of male Democrats under the null hypothesis that there is no association between party affiliation and gender can be calculated using the formula for the expected frequency in a contingency table. The formula is:
E = (Row Total × Column Total) / Grand Total
First, we find the totals for males, females, and each party affiliation:

• Total males = 300 (Democrat) + 500 (Republican) + 200 (Other) = 1000
• Total females = 600 (Democrat) + 300 (Republican) + 100 (Other) = 1000
• Total Democrats = 300 (Male) + 600 (Female) = 900
• Grand Total = 1000 (males) + 1000 (females) = 2000

We apply these values to the formula:
E = (Total males × Total Democrats) / Grand Total = (1000 × 900) / 2000 = 900,000 / 2000 = 450
Therefore, the expected number of male Democrats is 450.