Randomly selected students participated in an experiment to test their ability to determine when one minute(or sixty seconds) has passed. Forty students yielded a sample mean of 61.8 seconds.
Assuming that o= 11.7 seconds, Construct and interpret a 99% confidence interval estimate of the population mean of all
students. What is the 99% confidence interval for the population mean u.
618-+2.575*11.7/sqrt((40)) = (, )?
To construct a confidence interval for the population mean, we can use the formula:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
1. Find the critical value corresponding to a 99% confidence level. Since the sample size is small (n < 30), we can use the t-distribution table. With a 99% confidence level and the degrees of freedom (df = n - 1 = 40 - 1 = 39), the critical value is approximately 2.704.
2. Calculate the standard error. The standard error represents the standard deviation of the sample mean and is calculated as:
Standard Error = Sample Standard Deviation / Square Root of Sample Size
In this case, the sample standard deviation (o) is given as 11.7 seconds, and the sample size (n) is 40. Therefore:
Standard Error = 11.7 / √40 = 1.847 seconds.
3. Plug in the values into the confidence interval formula:
Confidence Interval = 61.8 ± (2.704 * 1.847)
Calculating the upper and lower bounds of the confidence interval:
Upper Bound = 61.8 + (2.704 * 1.847) = 66.90 seconds
Lower Bound = 61.8 - (2.704 * 1.847) = 56.70 seconds
4. Interpretation:
The 99% confidence interval estimate for the population mean of all students is between 56.70 seconds and 66.90 seconds. This means that we are 99% confident that the true average time for all students to determine when one minute has passed lies within this interval.