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 57.5 seconds. Assuming that sigmaequals9.2 ​seconds, construct and interpret a 95​% confidence interval estimate of the population mean of all students. hat is the 95​% confidence interval for the population mean mu​? Based on the​ result, is it likely that the​ students' estimates have a mean that is reasonably close to sixty​ seconds? A. ​Yes, because the confidence interval does not include sixty seconds. B. Yes​, because the confidence interval includes sixty seconds. C. ​No, because the confidence interval includes sixty seconds. D. No​, because the confidence interval does not include sixty seconds.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 57.5

Population standard deviation =    = 9.2

Sample size = n =40

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2 * ( /n)

= 1.96 * (9.2 /  40 )

E= 2.8511
At 95% confidence interval estimate of the population mean
is,

- E < < + E

57.5 - 2.8511 <   <57.5 + 2.8511

54.6489 <   < 60.3511

( 54.6489 , 60.3511 )

B. Yes​, because the confidence interval includes sixty seconds.