A human resources manager wants to determine a confidence interval estimate for the mean test score
for the next office-skills test to be given to a group of job applicants. In the past, the test scores have been
normally distributed with a mean of 74.2 and a standard deviation of 30.9. Determine a 95% confidence
interval estimate if there are 30 applicants in the group.
A. 63.14 to 85.26
B. 68.72 to 79.68
C. 13.64 to 134.76
D. 64.92 to 83.48
You need to find the error in the problem. You should have a formula that determines error. You also need to transform the 95% confidence interval into a z score in order to solve. Mean plus your error, mean minus your error should give you the correct confidence interval for the problem. Does this help?
To determine the confidence interval estimate for the mean test score, we can use the following formula:
Confidence Interval = Mean ± (Critical Value * Standard Error)
First, let's calculate the standard error, which is the standard deviation divided by the square root of the sample size:
Standard Error = standard deviation / √(sample size)
Standard Error = 30.9 / √30 ≈ 5.64
Next, we calculate the critical value, which depends on the desired confidence level and the sample size.
For a 95% confidence level and a sample size of 30, you can use a t-distribution with (n-1) degrees of freedom to find the critical value. Using a t-table or a calculator, the critical value for a 95% confidence level with 29 degrees of freedom is approximately 2.045.
Now we can calculate the confidence interval:
Confidence Interval = 74.2 ± (2.045 * 5.64)
Confidence Interval = 74.2 ± 11.52
Calculating the upper and lower bounds of the confidence interval:
Lower Bound = 74.2 - 11.52 ≈ 62.68
Upper Bound = 74.2 + 11.52 ≈ 85.72
Therefore, the 95% confidence interval estimate for the mean test score is approximately 62.68 to 85.72.
Comparing the calculated confidence interval with the options given:
A. 63.14 to 85.26 - Closest to the calculated interval
B. 68.72 to 79.68 - Not within the calculated interval
C. 13.64 to 134.76 - Not within the calculated interval
D. 64.92 to 83.48 - Not within the calculated interval
The correct answer is A. 63.14 to 85.26.