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 61.6 seconds. Assuming that sigma equals8.7 ​seconds, construct and interpret a 90 ​% confidence interval estimate of the population mean of all students. Click here to view a t distribution table. LOADING... Click here to view page 1 of the standard normal distribution table. LOADING... Click here to view page 2 of the standard normal distribution table. LOADING... What is the 90 ​% confidence interval for the population mean mu ​? nothing less thanmuless thannothing ​(Type integers or decimals rounded to one decimal place as​ needed.)

Answer 1

Solution :

Given that,

= 61.6

= 8.7

n = 40

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (8.7 / 40)

= 2.3

At 90% confidence interval estimate of the population mean is,

- E < < + E

61.6 - 2.3 < < 61.6 + 2.3

59.3 < < 63.9

(59.3 , 63.9)