An advertising company wants to determine if the cartoons series Voltes V, appeals to male viewers more than to female viewers. Based on random telephone interviews,it was found that 23 out of 48 males and 41 out of 90 females watch the series regularly. What should the advertising company conclude at the 5% level of significance?
For this problem we will use the Chi-squared distribution.
We would expent the percentages to be equal ie 0.4637 each, thus we would expect 22.26 males and 41.74 females to watch the program, we use this to calculate the Test statistic D^2
D^2 = SUM((Expected – observed)^2 / Expected)
= (22.26 – 23)^2/22.26 + (41.74 – 41)^2/41.74
=0.0246 + 0.0131
The Chi-Squared value for 1 degree of freedom at the 5% significance level is 3.841, thus 0.0377 is not larger than 3.841, thus we can conclude that gender has no effect on the viewership.