Question

7.3.36 : Question Help 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 60.1 seconds. Assuming that σ = 10.1 seconds, construct and interpret a 90% confidence interval estimate of the population mean ofal students. Click here to view a t distribution table. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. le. What is the 90% confidence interval for the population mean ? (Type integers or decimals rounded to one decimal place as needed.)

Answer 1

Solution:

We use z test here, since sample size is greater than 40. Also σ is known.

σ = 10.1

sample mean= x bar = 60.1

α= 0.10

α/2= 0.10/2 = 0.05

zα/2 = 1.645

Interval will be,

x bar - zα/2.σ/√n < μ < x bar + zα/2.σ/√n
60.1 - 1.645*(10.1/√40) < μ < 60.1 + 1.645*(10.1/√40)
60.1 - 2.63< μ < 61.1 + 2.63

57.47 < μ < 62.73

We can say that at 90%, μ lies between 57.47 and 62.73

So it is likely that students estimates have a mean that is reaonably close to 60 seconds.