Homework SourseMany companies use wellknown celebrities as spokespersons in
Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female 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 in the contingency table.
Male Celebrity Female Celebrity
Identified Product 41 61
Could not Identify 109 89
What is the calculated test statistic, rounded to four decimal places?
Solution
Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female 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 in the contingency table.
Male Celebrity Female Celebrity
Identified Product 41 61
Could not Identify 109 89
What is the calculated test statistic, rounded to four decimal places?
calculated test statistic = 5.9418
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
Total
fo-fe
R1
41
61
102
-10.0000
10.0000
R2
109
89
198
10.0000
-10.0000
Total
150
150
300
Expected Frequencies
Column variable
Row variable
C1
C2
Total
(fo-fe)^2/fe
R1
51.0000
51.0000
102
1.9608
1.9608
R2
99.0000
99.0000
198
1.0101
1.0101
Total
150
150
300
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
2
Degrees of Freedom
1
Results
Critical Value
3.8415
Chi-Square Test Statistic
5.9418
| Chi-Square Test | ||||||
| Observed Frequencies | ||||||
| Column variable | Calculations | |||||
| Row variable | C1 | C2 | Total | fo-fe | ||
| R1 | 41 | 61 | 102 | -10.0000 | 10.0000 | |
| R2 | 109 | 89 | 198 | 10.0000 | -10.0000 | |
| Total | 150 | 150 | 300 | |||
| Expected Frequencies | ||||||
| Column variable | ||||||
| Row variable | C1 | C2 | Total | (fo-fe)^2/fe | ||
| R1 | 51.0000 | 51.0000 | 102 | 1.9608 | 1.9608 | |
| R2 | 99.0000 | 99.0000 | 198 | 1.0101 | 1.0101 | |
| Total | 150 | 150 | 300 | |||
| Data | ||||||
| Level of Significance | 0.05 | |||||
| Number of Rows | 2 | |||||
| Number of Columns | 2 | |||||
| Degrees of Freedom | 1 | |||||
| Results | ||||||
| Critical Value | 3.8415 | |||||
| Chi-Square Test Statistic | 5.9418 |
