Chapter 10: Q.10.132 (page 443)

Measuring Treadwear. Refer to Exercise 10.126 and find a $95 %$ confidence interval for the mean difference in measurement by the weight and groove methods.

Short Answer

Expert verified

$(1.59, 5.92)$ is the data's $95 %$ confidence interval.

Step by step solution

Given Information

The given data is,

$\begin{matrix} Method & Method \\ 30.5 & 28.7 \\ 30.9 & 25.9 \\ 31.9 & 23.3 \\ 30.4 & 23.1 \\ 27.3 & 23.7 \\ 20.4 & 20.9 \\ 24.5 & 16.1 \\ 20.9 & 19.9 \\ 18.9 & 15.2 \\ 13.7 & 11.5 \\ 11.4 & 11.2 \end{matrix}$

Explanation

Below is the given data,

$\begin{matrix} Method & Method & Difference = d & d^{2} \\ 30.5 & 28.7 & 1.8 & 3.24 \\ 30.9 & 25.9 & 5 & 25 \\ 31.9 & 23.3 & 8.6 & 73.96 \\ 30.4 & 23.1 & 7.3 & 53.29 \\ 27.3 & 23.7 & 3.6 & 12.96 \\ 20.4 & 20.9 & - 0.5 & 0.25 \\ 24.5 & 16.1 & 8.4 & 70.56 \\ 20.9 & 19.9 & 1 & 1 \\ 18.9 & 15.2 & 3.7 & 13.69 \\ 13.7 & 11.5 & 2.2 & 4.84 \\ 11.4 & 11.2 & 0.2 & 0.04 \\ 41.3 & 258.83 \end{matrix}$

Explanation

The sample mean is,

$\bar{d} = \frac{\sum d}{n}$

$= \frac{41.3}{11}$

localid="1651285684383" $= 3.7545$

The standard deviation is,

$s_{d} = \sqrt{\frac{\sum d_{i}^{2} - \frac{{(\sum d_{i})}^{2}}{n}}{n - 1}}$

$= \sqrt{\frac{258.83 - \frac{(44.3)^{2}}{11}}{11 - 1}}$

$= 3.2213$

Explanation

The degree of freedom is,

$dof = n - 1$

$= 11 - 1$

$= 10$

The level of significance's critical value is $\pm 2.228$ .

The confidence level is,

$C I = \bar{d} \pm t_{\frac{a}{2}} \frac{s_{d}}{\sqrt{n}}$

$= 3.7545 \pm (2.228) \frac{3.2213}{\sqrt{11}}$

$= (1.59, 5.92)$

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Measuring Treadwear. Refer to Exercise 10.126 and find a $95 %$ confidence interval for the mean difference in measurement by the weight and groove methods.

Short Answer

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Measuring Treadwear. Refer to Exercise 10.126 and find a 95% confidence interval for the mean difference in measurement by the weight and groove methods.

Short Answer

Step by step solution

Given Information

Explanation

Explanation

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Geometry

Applied Mathematics

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Measuring Treadwear. Refer to Exercise 10.126 and find a $95 %$ confidence interval for the mean difference in measurement by the weight and groove methods.