Question

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 61.5 seconds. Assuming that σ = 10.6 ​seconds, construct and interpret a 95​% confidence interval estimate of the population mean of all students.

What is the 95​% confidence interval for the population mean μ​?

Based on the​ result, is it likely that the​ students' estimates have a mean that is reasonably close to sixty​ seconds?

Answer 1

Solution:

Here, we have to find the 95% confidence interval for the population mean.

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given data, we have

Xbar = 61.5

σ = 10.6

n = 40

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 61.5 ± 1.96*10.6/sqrt(40)

Confidence interval = 61.5 ± 1.96* 1.676007

Confidence interval = 61.5 ± 3.284974

Lower limit = 61.5 - 3.284974 = 58.21503

Upper limit = 61.5 + 3.284974 =64.78497

Confidence interval = (58.22, 64.78)

Based on the result, it is likely that the students’ estimates have a mean that is reasonably close to sixty seconds because above confidence interval includes the value 60.