Question

7

A car manufacturer is interested in estimating the true mean fuel consumption in real-world city driving for one of its new models. 10 new randomly selected cars are driven for a tank, and it is found that the sample mean fuel consumption is 9.4 l/100k, with a sample standard deviation of s = 0.343. Suppose the manufacturer wishes to construct a confidence interval for mu, the true mean fuel consumption for this model under these conditions. a) What is the margin of error of a 95% confidence interval for mu? Round your response to at least 3 decimal places. Number b) What is the margin of error of a 90% confidence interval for mu? Round your response to at least 3 decimal places. Number

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 9.4

sample standard deviation = s = 0.343

sample size = n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

a) At 95% confidence level

$\alpha$ = 1 - 95%

$\alpha$ =1 - 0.95 =0.05

$\alpha$/2 = 0.025

t$\alpha$/2,df = t_0.025,9 = 2.262

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 2.262 * ( 0.343 / $\sqrt$ 10)

Margin of error = E = 0.245

b) At 90% confidence level

$\alpha$ = 1 - 90%

$\alpha$ =1 - 0.90 =0.10

$\alpha$/2 = 0.05

t$\alpha$/2,df = t_0.05,9 = 1.833

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 1.833 * ( 0.343 / $\sqrt$ 10)

Margin of error = E = 0.199