Question 1185621: John Isaac Inc., a designer and installer of industrial signs, employs 60 people. The company recorded the type of the most recent visit to a doctor by each employee. A recent national survey found that 53% of all physician visits were to primary care physicians, 19% to medical specialists, 17% to surgical specialists, and 11% to emergency departments. Test at the .01 significance level if Isaac employees differ significantly from the survey distribution. Here are their results:
Primary care 29
Medical specialist 11
Surgical specialist 16
Emergency 4
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. State the Hypotheses:**
* **Null Hypothesis (H₀):** The distribution of doctor visits for Isaac employees is the same as the national survey distribution.
* **Alternative Hypothesis (H₁):** The distribution of doctor visits for Isaac employees is different from the national survey distribution.
**2. Calculate Expected Frequencies:**
We need to find the expected number of employees who visited each type of doctor based on the national survey percentages:
* **Primary Care:** 0.53 * 60 = 31.8
* **Medical Specialist:** 0.19 * 60 = 11.4
* **Surgical Specialist:** 0.17 * 60 = 10.2
* **Emergency:** 0.11 * 60 = 6.6
**3. Calculate the Chi-Square Statistic:**
χ² = Σ [(Observed - Expected)² / Expected]
χ² = (29 - 31.8)² / 31.8 + (11 - 11.4)² / 11.4 + (16 - 10.2)² / 10.2 + (4 - 6.6)² / 6.6
χ² ≈ 0.245 + 0.014 + 3.294 + 1.030
χ² ≈ 4.583
**4. Determine Degrees of Freedom:**
Degrees of freedom (df) = Number of categories - 1 = 4 - 1 = 3
**5. Find the Critical Value:**
Since we are testing at the 0.01 significance level, we need to find the critical value from a Chi-Square distribution table with df = 3 and α = 0.01. The critical value is approximately 11.345.
**6. Make a Decision:**
* **Decision:** Since the calculated Chi-Square statistic (4.583) is less than the critical value (11.345), we fail to reject the null hypothesis.
* **Interpretation:** There is not enough evidence to conclude that the distribution of doctor visits for Isaac employees differs significantly from the national survey distribution at the 0.01 significance level.
**Conclusion:**
Although there are some differences between the observed and expected frequencies, they are not large enough to be statistically significant at the 0.01 level. The data does not provide strong evidence to suggest that Isaac employees' doctor visit patterns are different from the national trends.
|
|
|
