One hundred subjects in a psychological study had a mean of 35 on a test instrument designed to measure anger. The study the ó=10. Find a 99% confidence interval for the mean anger score of the population.
To find the 99% confidence interval for the mean anger score of the population, we can use the following formula:
Confidence Interval = X̄ ± Z * (σ / √n)
Where:
X̄ = sample mean
Z = z-score corresponding to the desired confidence level
σ = population standard deviation
n = sample size
In this case, we are given:
X̄ = 35 (mean of the sample)
σ = 10 (standard deviation of the population)
n = 100 (sample size)
To determine the z-score corresponding to a 99% confidence level, we need to look up the value in the z-table or use a statistical calculator. The z-score for a 99% confidence level is approximately 2.575.
Now we can plug in the values into the formula:
Confidence Interval = 35 ± 2.575 * (10 / √100)
Simplifying further:
Confidence Interval = 35 ± 2.575 * 1
Finally, the confidence interval is:
Confidence Interval = 35 ± 2.575
Therefore, the 99% confidence interval for the mean anger score of the population is (32.425, 37.575).