Question

2. According to the American Psychological Association, the average salary among the population of female members of the APA is less than $51,500, the average of all comparable members who have a doctorate and teach full-time. Given a sample of 100 female members, the average salary was estimated to be $50,300. According to the APA, the standard deviation of the salary of all members is $3,000 A. Determine the 99% confidence interval for the estimate of the average salary of all female members of the APA. B. Interpret the interval

Answer 1

The 99% confidence interval for the average salary of all female APA members is between $49,527 and $51,073. This interval indicates with 99% confidence where the true average salary falls.

Step-by-step explanation:

To determine the 99% confidence interval for the estimate of the average salary of all female members of the American Psychological Association (APA), we use the formula for the confidence interval of the mean when the standard deviation is known:

CI = ± Z * (σ/ √n)

Where:

• CI is the confidence interval
• Z is the Z-score corresponding to the desired confidence level
• σ is the population standard deviation
• n is the sample size

Given data:

• Sample mean (μ) = $50,300
• Population standard deviation (σ) = $3,000
• Sample size (n) = 100
• Z-score for 99% confidence = 2.576 (from Z-table)

Calculate the margin of error (ME):

ME = Z * (σ/ √n) = 2.576 * ($3,000/ √100) = 2.576 * $300 = $773

Now, calculate the confidence interval:

Lower Limit = Sample mean - ME = $50,300 - $773 = $49,527

Upper Limit = Sample mean + ME = $50,300 + $773 = $51,073

Interpretation of the Interval: The 99% confidence interval means that we can be 99% confident that the true average salary of all female APA members lies between $49,527 and $51,073.