Question

Dylan Jones kept careful records of the fuel efficiency of his new car. After the first eleven times he filled up the tank, he found the mean was 27.3 miles per gallon (mpg) with a sample standard deviation of 1.3 mpg. Compute the 95% confidence interval for his mpg. (Use t Distribution Table.) (Round your answers to 3 decimal places.) How many times should he fill his gas tank to obtain a margin of error below 0.15 mpg? (Use z Distribution Table.) (Round your answer to the next whole number.)

Answer 1

Solution :

Given that,

= 27.3

s =1.3

n = Degrees of freedom = df = n - 1 = 11- 1 = 10

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,10 = 2.228 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 2.228* (1.3 / 11)

= 0.87

The 95% confidence interval is,

- E < < + E

27.3 - 0.87< < 27.3+ 0.87

26.43 < < 28.17

( 26.43 , 28.17)

part b

Solution

standard deviation =s =1.3

Margin of error = E = 0.15

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = [Z/2* / E] 2

n = ( 1.96*1.3 / 0.15 )2

n =289

Sample size = n =289