Question

The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 25.25 mpg and a standard deviation of σ = 2.00 mpg.

(a) What is the standard error of X⎯⎯⎯X¯ , the mean from a random sample of 9 fill-ups by one driver? (Round your answer to 4 decimal places.)
  
Standard error of    X⎯⎯⎯X¯             

(b) Within what interval would you expect the sample mean to fall, with 95 percent probability? (Round your answers to 4 decimal places.)
  
The interval is from ? to ?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 25.25

Population standard deviation =    = 2.0

Sample size = n = 9

Standard error = ( /n) = ( 2 /9 ) = 0.6667

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z_{0.025 = 1.96}

Z/2 = 1.96

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

= 1.96 * (2 / 9 )

= 1.3066

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

- E < < + E

25.25 - 1.3066 < < 25.25 + 1.3066

23.9434 < < 26.5566


The interval is 23.9434 to 26.5566