A sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. Construct a 95% confidence interval for the average starting salary of all attorneys in the city.

A. (89869.82, 114814.18)
B. (91331.94, 113352.06)
C. (90292.73, 114391.27)
D. (90371.37, 114312.63)

B. (91331.94, 113352.06)

To construct a 95% confidence interval for the average starting salary of all attorneys in New York City, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

1. Calculate the standard error:
Standard Error = standard deviation / sqrt(sample size)
= 21756 / sqrt(15)
≈ 5607.95

2. Determine the critical value associated with a 95% confidence level. Since we have a small sample size (n < 30), we need to use a t-distribution and degrees of freedom (df) equal to n - 1.
Using a t-table or calculator, with df = 14 and a 95% confidence level, the critical value is approximately 2.145.

3. Calculate the confidence interval:
Confidence Interval = 102342 ± (2.145 * 5607.95)
= (102342 - 12025.34, 102342 + 12025.34)
= (90216.66, 114467.34)

Therefore, the correct answer is C. (90292.73, 114391.27)

To construct a confidence interval for the average starting salary of all attorneys in New York City, we will use the formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / sqrt(sample size))

First, let's identify the components we need for the formula:

Sample mean (x̄) = $102,342
Standard deviation (σ) = $21,756
Sample size (n) = 15
Critical value:
- Since we have a sample size of 15, which is relatively small, we need to use a t-distribution.
- We want a 95% confidence interval, so we need to find the critical t-value with 14 degrees of freedom (df = n - 1) and a confidence level of 95%.

Looking up the t-distribution table or using a calculator, the critical t-value for a 95% confidence level and 14 degrees of freedom is approximately 2.145.

Now we can calculate the confidence interval:

Confidence Interval = $102,342 ± (2.145) * ($21,756 / sqrt(15))

Confidence Interval ≈ $102,342 ± (2.145) * ($5,623.75)

Confidence Interval ≈ $102,342 ± $12,067.63

Confidence Interval ≈ ($90,274.37, $114,409.63)

Therefore, the correct answer is option C: ($90,274.37, $114,409.63).