Question

Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below. The appropriate value of Test Statistic is __________ .

Answer 1

chi^2 (X^2) test statistic will be used, as per the following steps procedure, and summary will be given based on its calculated & critical value

Explanation:

The test statistic chi^2 (X^2) is used to test the relationship between two categorical variables. In given case, companies want to analyse whether celebrities' gender in advertisements affect the brand awareness among public. Chi^2 (X^2) will be used as test statistic in the case, because it involves categorical variables - male or female celebrities, brand identified or not identified.

• Matrix of celebrities gender & awareness level will be used for following formula.
• Null Hypothesis [H0] = Rows & columns, or celebrity gender & brand recognition are unrelated
• Alternate Hypothesis [H1] = Rows & columns, or celebrity gender & brand recognition are related

(X^2) = [Observed count - Expected Count]^2 / Observed count, where observed count = [ (Row Total) (Column Total)] / Grand Total

• If Chi^2 test statistic calculated value > tabulated critical value at significance level, we reject null hypothesis & state that celebrity gender & brand recognition are related
• If chi^2 test statistic calculated value < tabulated critical value at significance level, we don't reject null hypothesis & state that celebrity gender & brand recognition are unrelated