Chapter 9: Q. 82 (page 543)

Refer to Exercise $9.119$ . Conduct a hypothesis test to see if your decision and conclusion would change if your belief were that the brown trout's mean I.Q is not four.

Short Answer

Expert verified

The brown trout's mean I.Q is not four.

Step by step solution

Introduction

Null hypotheses is,

$H_{0} : μ = 4$

Alternative hypotheses is,

$H_{0} : μ \neq 4$

The random variable $\bar{X}$ is the average $I . Q .$

$n - 1 = 11$

Sample mean is,

$\bar{x} = \frac{5 + 4 + \dots + 8 + 5}{12}$

$= 4.92$

Sample standard deviation is,

$s = \sum_{j = 1}^{n} \frac{{(x_{j} - \bar{x})}^{2}}{n - 1}$

$= \sum_{j = 1}^{12} \frac{{(x_{j} - 4.92)}^{2}}{11}$

$= 1.62$

Test is,

$t_{11} = \frac{4.92 - 4}{1.62 / \sqrt{12}}$

$= 1.958$

Explanation

We do not reject the null hypothesis when the $p$ value is bigger than the established alpha value.

$p -value = 0.076 > 0.05$

$= α$

Mean and variance of random is,

$\bar{x} - t_{\frac{α}{2}, n - 1} \frac{s}{\sqrt{n}} \leq μ \leq \bar{x} + t_{\frac{α}{2}, n - 1} \frac{s}{\sqrt{n}} . . . . . . 1$

where $t_{\frac{α}{2}, n - 1}$ is the upper

$100 \frac{α}{2}$ percentage point of the distribution with $n - 1$ degrees of freedom.

$\frac{α}{2} = 0.025$

$\Rightarrow t_{\frac{a}{2}, n - 1} = t_{0.025, 11}$

$= 2.2 . . . . . . . 2$

From $1$ and $2$ ,

$4.92 - 2.2 \frac{1.62}{\sqrt{12}} \leq μ \leq 4.92 + 2.2 \frac{1.62}{\sqrt{12}}$

$4.92 - 2.2 \times 0.468 \leq μ \leq 4.92 + 2.2 \times 0.468$

Population proportion is,

$3.886 \leq μ \leq 5.947$

Therefore, Mean I.Q is not four $(4) .$

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Refer to Exercise $9.119$ . Conduct a hypothesis test to see if your decision and conclusion would change if your belief were that the brown trout's mean I.Q is not four.

Short Answer

Step by step solution

Introduction

Explanation

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Refer to Exercise 9.119. Conduct a hypothesis test to see if your decision and conclusion would change if your belief were that the brown trout's mean I.Q is not four.

Short Answer

Step by step solution

Introduction

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Probability and Statistics

Statistics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Refer to Exercise $9.119$ . Conduct a hypothesis test to see if your decision and conclusion would change if your belief were that the brown trout's mean I.Q is not four.