Chapter 10: Q.10.133 (page 443)

Glaucoma and Corneal Thickness. Refer to Exercise 10.127 and obtain an $80 %$ confidence interval for the difference between the mean corneal thickness of normal eyes and that of eyes with glaucoma.

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

The table is shown below,

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

Explanation

The sample mean is,

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

$= \frac{41.3}{11}$

$= 3.7545$

The standard deviation is,

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

$= \sqrt{\frac{258.83 - \frac{(41.3)^{2}}{11}}{11 - 1}}$

$= 3.2213$

Explanation

The degree of freedom is,

$dof = n - 1$

$= 11 - 1$

$= 10$

The critical value for level of significance 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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Glaucoma and Corneal Thickness. Refer to Exercise 10.127 and obtain an $80 %$ confidence interval for the difference between the mean corneal thickness of normal eyes and that of eyes with glaucoma.

Short Answer

Step by step solution

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Explanation

Explanation

Explanation

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Glaucoma and Corneal Thickness. Refer to Exercise 10.127 and obtain an80% confidence interval for the difference between the mean corneal thickness of normal eyes and that of eyes with glaucoma.

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

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

Glaucoma and Corneal Thickness. Refer to Exercise 10.127 and obtain an $80 %$ confidence interval for the difference between the mean corneal thickness of normal eyes and that of eyes with glaucoma.