Model Answer
0 min readIntroduction
The Chi-Square test is a statistical method used to determine if there is a significant association between two categorical variables. In marketing and audience research, it’s crucial to understand whether a product, like a movie, appeals differently to various demographic segments. This allows for targeted advertising and resource allocation. The producer’s inquiry necessitates a hypothesis test to ascertain if the observed distribution of movie appeal across age groups differs significantly from what would be expected if appeal were uniform across all age groups. This analysis will help optimize the advertising campaign for maximum impact.
Understanding the Chi-Square Test
The Chi-Square test assesses the independence of two categorical variables. The null hypothesis (H0) assumes that the variables are independent (movie appeal is not related to age group). The alternative hypothesis (H1) states that the variables are dependent (movie appeal is related to age group). The test statistic measures the discrepancy between observed and expected frequencies.
Observed Frequencies (Assume Data)
Since the question doesn't provide the observed data, we'll assume a sample dataset for demonstration. Let's assume the producer surveyed 200 people and categorized them into four age groups (18-25, 26-35, 36-45, 46+) and recorded whether they liked the movie (Yes/No).
| Age Group | Liked Movie (Yes) | Liked Movie (No) | Total |
|---|---|---|---|
| 18-25 | 30 | 20 | 50 |
| 26-35 | 40 | 10 | 50 |
| 36-45 | 25 | 25 | 50 |
| 46+ | 15 | 30 | 45 |
| Total | 110 | 85 | 195 |
Calculating Expected Frequencies
Expected frequency for each cell is calculated as: (Row Total * Column Total) / Grand Total. For example, the expected frequency for the '18-25' age group and 'Liked Movie (Yes)' is (50 * 110) / 195 = 28.21.
| Age Group | Liked Movie (Yes) - Expected | Liked Movie (No) - Expected |
|---|---|---|
| 18-25 | 28.21 | 21.79 |
| 26-35 | 37.95 | 12.05 |
| 36-45 | 32.82 | 17.18 |
| 46+ | 21.02 | 23.98 |
Calculating the Chi-Square Statistic
The Chi-Square statistic is calculated as: Σ [(Observed - Expected)² / Expected].
χ² = [(30-28.21)²/28.21] + [(20-21.79)²/21.79] + [(40-37.95)²/37.95] + [(10-12.05)²/12.05] + [(25-32.82)²/32.82] + [(25-17.18)²/17.18] + [(15-21.02)²/21.02] + [(30-23.98)²/23.98]
χ² = 0.32 + 0.21 + 0.10 + 0.44 + 2.34 + 3.53 + 1.46 + 1.83 = 10.23
Decision and Interpretation
The calculated Chi-Square statistic is 10.23. The critical value for 6 degrees of freedom (number of age groups - 1 = 3, and number of responses - 1 = 2, total 3+2 = 5, but since we have 4 age groups, df = (4-1)*(2-1) = 3, and since we have 2 responses, df = (2-1) = 1, so total df = 3+1 = 4. However, the question states 6 degrees of freedom) and a 5% significance level is 12.592. Since 10.23 < 12.592, we fail to reject the null hypothesis.
This indicates that there is not enough evidence to conclude that movie appeal is significantly different across the age groups. The producer cannot confidently say that the movie appeals more to a specific age group than to others based on this sample.
Conclusion
In conclusion, based on the Chi-Square test and the provided (assumed) data, the producer does not have sufficient statistical evidence to suggest that the movie’s appeal varies significantly across different age groups. This implies that the advertising campaign can be designed to target all age groups equally, or further research with a larger sample size might be needed to detect subtle differences. The decision to reject or accept the null hypothesis is crucial for effective marketing strategy.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.