Your statistics instructor wants you to determine a confindence interval estimate for the mean test score for the next exam. In the past, the test scores have been normally distributed with a mean of 74.2 and a standard deviation of 30.9. A 95% confidence interval estimate if your class has 30 students is?
To determine a confidence interval estimate for the mean test score for the next exam, we can use the formula:
Confidence interval = mean ± (Z * (standard deviation / √n))
where:
mean = 74.2 (mean of past test scores)
standard deviation = 30.9 (standard deviation of past test scores)
n = 30 (number of students in the class)
Z = Z-score corresponding to the desired confidence level (95% in this case)
First, we need to find the Z-score for a 95% confidence level. The Z-score can be obtained using a standard normal distribution table or a statistical calculator. The Z-score for a 95% confidence level is approximately 1.96.
Next, we substitute the values into the formula:
Confidence interval = 74.2 ± (1.96 * (30.9 / √30))
Calculating the square root of 30 (√30) gives approximately 5.48.
Now we can substitute this value into the formula:
Confidence interval = 74.2 ± (1.96 * (30.9 / 5.48))
Simplifying the expression:
Confidence interval = 74.2 ± (1.96 * 5.63)
Calculating the product of 1.96 and 5.63 gives approximately 11.03.
Finally, we can calculate the confidence interval:
Confidence interval = 74.2 ± 11.03
This gives us a 95% confidence interval estimate for the mean test score for the next exam as (63.17, 85.23).