SOLUTION: A dentist is interested in the proportion of adults who have had their wisdom teeth removed. To determine this, a random sample of {227} adults was collected and it was found that

Click here to see ALL problems on Probability-and-statistics

Question 1197733: A dentist is interested in the proportion of adults who have had their wisdom teeth removed. To determine this, a random sample of {227} adults was collected and it was found that {105} still had their wisdom teeth.
Using this information construct an approximate 90% confidence interval for the proportion of adults who have had their wisdom teeth removed.
Answer by proyaop(69) (Show Source):
You can put this solution on YOUR website!
**1. Calculate the Sample Proportion (p̂)**
* p̂ = (Number of adults who have had wisdom teeth removed) / (Sample size)
* p̂ = (227 - 105) / 227
* p̂ = 122 / 227
* p̂ ≈ 0.537
**2. Find the Critical Value (z*)**
* For a 90% confidence interval, the critical value (z*) is 1.645. This value corresponds to the z-score that captures 90% of the data within two standard deviations of the mean in a standard normal distribution.
**3. Calculate the Standard Error**
* Standard Error (SE) = √(p̂ * (1 - p̂) / n)
* where:
* p̂ = sample proportion (0.537)
* n = sample size (227)
* SE = √(0.537 * (1 - 0.537) / 227)
* SE ≈ 0.033
**4. Calculate the Margin of Error**
* Margin of Error (ME) = z* * SE
* ME = 1.645 * 0.033
* ME ≈ 0.054
**5. Construct the Confidence Interval**
* Lower Limit = p̂ - ME = 0.537 - 0.054 = 0.483
* Upper Limit = p̂ + ME = 0.537 + 0.054 = 0.591
**Therefore, the 90% confidence interval for the proportion of adults who have had their wisdom teeth removed is (0.483, 0.591).**
**Interpretation:**
We are 90% confident that the true proportion of adults who have had their wisdom teeth removed lies between 48.3% and 59.1%.