Chapter 10: Q.10.129 (page 443)

Zea Mays. Refer to Exercise 10.123.
a. Determine a $95 %$ confidence interval for the difference between the mean heights of cross-fertilized and self-fertilized Zea mays.
b. Repeat part (a) for a $99 %$ confidence level.

Short Answer

Expert verified

a). $(0.0303, 41.8297)$ is the $95 %$ confidence interval for the data

b). $(- 8.0776, 49.9376)$ is the $99 %$ confidence interval for the data.

Step by step solution

Part (a) Step 1: Given Information

The values are $\bar{d} = 20.93, s_{d} = 37.74$ , the level of significance is $0.05$ , the data is shown below.

$49$	$- 67$	$8$	$16$	$6$
$23$	$28$	$41$	$14$	$29$
$56$	$24$	$75$	$60$	$- 48$

Part (a) Step 2: Explanation

The degree of freedom is,

$dof = n - 1$

$= 15 - 1$

$= 14$

The level of significant crucial value is $\pm 2.145$ .

Therefore, we can compute the confidence level as follow:

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

$= 20.93 \pm (2.145) \frac{37.74}{\sqrt{15}}$

$= (0.0303, 41.8297)$

Part (b) Step 1: Given Information

The values are $\bar{d} = 20.93, s_{d} = 37.74$ ,

the significance level is $0.05$ , the data is shown as follow.

$49$	$- 67$	$8$	$16$	$6$
$23$	$28$	$41$	$14$	$29$
$56$	$24$	$75$	$60$	$- 48$

Part (b) Step 2: Explanation

Let's compute the degree of freedom:

$dof = n - 1$

$= 15 - 1$

$= 14$

The level of significant crucial value is $\pm 2.977$ .

Therefore, we can compute the confidence level as follow,

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

$= 20.93 \pm (2.977) \frac{37.74}{\sqrt{15}}$

$= (- 8.0776, 49.9376)$

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Zea Mays. Refer to Exercise 10.123.
a. Determine a $95 %$ confidence interval for the difference between the mean heights of cross-fertilized and self-fertilized Zea mays.
b. Repeat part (a) for a $99 %$ confidence level.

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Explanation

Part (b) Step 1: Given Information

Part (b) Step 2: Explanation

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Zea Mays. Refer to Exercise 10.123.a. Determine a 95% confidence interval for the difference between the mean heights of cross-fertilized and self-fertilized Zea mays.b. Repeat part (a) for a 99% confidence level.

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Explanation

Part (b) Step 1: Given Information

Part (b) Step 2: Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Probability and Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Zea Mays. Refer to Exercise 10.123.
a. Determine a $95 %$ confidence interval for the difference between the mean heights of cross-fertilized and self-fertilized Zea mays.
b. Repeat part (a) for a $99 %$ confidence level.