A study of 40 psychology teachers showed that they spent, on average, 12.6 minutes correcting a student's final term paper. Find the 90 percent confidence interval of the mean time for all psychology teachers correcting final term papers when the deviation is 2.5.
Formula:
CI90 = mean ± 1.645(s/√n)
mean = 12.6
s = 2.5
n = 40
Plug the values into the formula and calculate the interval.
To find the 90 percent confidence interval of the mean time for all psychology teachers correcting final term papers, we can use the formula:
Confidence Interval = X̄ ± Z * (σ/√n)
Where:
- X̄ is the sample mean
- Z is the Z-score corresponding to the desired confidence level (in this case, 90 percent)
- σ is the population standard deviation
- n is the sample size
In this case, we have:
- Sample mean (X̄) = 12.6 minutes
- Population standard deviation (σ) = 2.5 minutes
- Sample size (n) = 40
First, we need to find the Z-score for a 90 percent confidence level. We can look up this value in a standard normal distribution table or use a Z-score calculator. The Z-score for a 90 percent confidence level is approximately 1.645.
Now we can substitute the values into the formula to calculate the confidence interval:
Confidence Interval = 12.6 ± 1.645 * (2.5/√40)
Calculating the values:
Confidence Interval = 12.6 ± 1.645 * (2.5/√40)
Confidence Interval = 12.6 ± 1.645 * (2.5/6.324)
Confidence Interval = 12.6 ± 1.645 * 0.396
Confidence Interval = 12.6 ± 0.651
Therefore, the 90 percent confidence interval for the mean time spent by all psychology teachers correcting final term papers is approximately (11.949, 13.251) minutes.