Question 1195841: In one survey, successful female entrepreneurs were asked to state their personal definition of success in terms of several categories from which they could select. Thirty-nine per cent responded that happiness was their definition of success, 12% said that sales/profit was their definition, 18% responded that helping others was their definition, and 31% responded that achievements/challenge was their definition. Suppose you wanted to determine whether male entrepreneurs felt the same way and took a random sample of men, resulting in the following data. Use the chi-square goodness of fit test to determine whether the observed frequency distribution of data for men is the same as for women. Use 5% level of significance
Definition
Observed frequency
Happiness
40
Sales/profit
90
Helping others
30
Achievement/challenges
60
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! **1. Set up Hypotheses**
* **Null Hypothesis (H0):** The distribution of success definitions for male entrepreneurs is the same as that for female entrepreneurs.
* **Alternative Hypothesis (H1):** The distribution of success definitions for male entrepreneurs is different from that for female entrepreneurs.
**2. Calculate Expected Frequencies**
* **Total Sample Size:** 40 + 90 + 30 + 60 = 220
* **Expected Frequencies:**
* Happiness: 220 * 0.39 = 85.8
* Sales/Profit: 220 * 0.12 = 26.4
* Helping Others: 220 * 0.18 = 39.6
* Achievement/Challenges: 220 * 0.31 = 68.2
**3. Calculate Chi-Square Test Statistic**
* **Formula:** χ² = Σ [(Observed Frequency - Expected Frequency)² / Expected Frequency]
* **Calculations:**
* Happiness: (40 - 85.8)² / 85.8 ≈ 23.67
* Sales/Profit: (90 - 26.4)² / 26.4 ≈ 155.09
* Helping Others: (30 - 39.6)² / 39.6 ≈ 2.43
* Achievement/Challenges: (60 - 68.2)² / 68.2 ≈ 1.01
* **Total Chi-Square:** 23.67 + 155.09 + 2.43 + 1.01 = 182.20
**4. Determine Degrees of Freedom**
* Degrees of Freedom (df) = Number of Categories - 1 = 4 - 1 = 3
**5. Find Critical Value**
* Using a chi-square distribution table with df = 3 and α = 0.05, the critical value is approximately 7.815.
**6. Decision**
* Since the calculated chi-square statistic (182.20) is greater than the critical value (7.815), we reject the null hypothesis.
**7. Conclusion**
* There is sufficient evidence at the 5% significance level to conclude that the distribution of success definitions for male entrepreneurs is significantly different from that for female entrepreneurs.
**Note:**
* This analysis assumes that the sample of male entrepreneurs is representative of the population of male entrepreneurs.
* The chi-square test requires expected frequencies to be at least 5 in each category. This condition is met in this case.
**Interpretation:**
* The results suggest that male entrepreneurs may prioritize different aspects of success compared to female entrepreneurs.
* Further investigation could explore the specific factors that contribute to these differences.
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