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

59.4 seconds. Assuming that

sigmaσ=10.3

​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 u?

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

Answer 1

Fundamentals: - mean if known confidence population is given interval standard by for a population deviation (o) is u = y 2 72 l= population mean X= Sample mean. a= level of significance os population standaod devitations Ana Sample Size : solu - Given X = 59.4 n 40 or = 10.3 do 1-0.95 +0.05 2(0.005) using z-table = 1.96 pole Ft 2101095) M = 59.4+ 1.96 X 10.3 Juo

M = 59.4 I 3.192 de= ( 56.208 69.598) so 954. confidence interval is 56.11 cu < 62.59 1 Interpret !- we are ast. confident that population mean falls in this interval → Now 60 seconds comes in this interval so (yes] it is likely that student's mean - i i close to sixty 6o.