Chapter 8: Q 8.86 (page 333)

Fuel Expenditures. In estimating the mean monthly fuel expenditure, $μ$ , per household vehicle, the Energy Information $Ad -$ ministration takes a sample of size $6841$ . Assuming that $σ = $ 20.65$ . determine the margin of error in estimating $μ$ at the $95 %$ level of confidence.

Short Answer

Expert verified

Margin of Error is $956 %$ and confidence level is $$ 0.49$ .

Step by step solution

Given Information

It is given that

$n = 6841$

$σ = $ 20.65$

Calculations to be done at $95 %$ confidence level.

Determination of Za2

Margin of Error at $95 %$ confidence level is

$1 - α = 0.95$

$\Rightarrow α = 0.05$

$\Rightarrow \frac{α}{2} = 0.025$

Hence, $Z_{\frac{a}{2}} = Z_{0.025} = 1.96$

Calculation of Margin of Error

At $95 %$ confidence level, Margin of Error is
$E = Z_{0.025} \times \frac{σ}{\sqrt{n}}$

$E = 1.96 \times \frac{20.65}{\sqrt{6841}} = 0.49$

Required Margin of Error is $$ 0.49$

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Fuel Expenditures. In estimating the mean monthly fuel expenditure, $μ$ , per household vehicle, the Energy Information $Ad -$ ministration takes a sample of size $6841$ . Assuming that $σ = $ 20.65$ . determine the margin of error in estimating $μ$ at the $95 %$ level of confidence.

Short Answer

Step by step solution

Given Information

Determination of Za2

Calculation of Margin of Error

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Fuel Expenditures. In estimating the mean monthly fuel expenditure, μ, per household vehicle, the Energy Information Ad- ministration takes a sample of size 6841. Assuming that σ=$20.65. determine the margin of error in estimating μ at the 95% level of confidence.

Short Answer

Step by step solution

Given Information

Determination of Za2

Calculation of Margin of Error

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Logic and Functions

Statistics

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Fuel Expenditures. In estimating the mean monthly fuel expenditure, $μ$ , per household vehicle, the Energy Information $Ad -$ ministration takes a sample of size $6841$ . Assuming that $σ = $ 20.65$ . determine the margin of error in estimating $μ$ at the $95 %$ level of confidence.