Chapter 14: Q. 14.123 (page 585)

For each exercise, decide at $10 %$ significance level, whether the data provide sufficient evidence to reject the null hypothesis in favor of alternate hypothesis.
$H_{a} : ρ \neq 0$

Short Answer

Expert verified

We reject the null hypothesis $H_{a} : ρ \neq 0$ , the variables are not linearly correlated.

Step by step solution

Step 1. Correlation Coefficient

Sample correlation coefficient is calculated by

$r = \sum_{} z x z y / (n - 1)$

where, $z x_{n} = (x_{n -} x m e a n) / s \tan d a r d d e v i a t i o n$ and same for $z y_{n}$

So, $r = - 0.6325$

Step 2. Hypothesis Testing

$r \neq 0$ for sample needs to be tested using hypothesis testing, to ensure that the population correlation parameter $ρ (r h o) \neq 0$

$t = r / \sqrt{(1 - r^{2}) / (n - 2)} = - 0.6325 / \sqrt{0.599 / 3} = - 0.6325 / 0.4468 t = - 1.415$

As $t$ value is smaller and $p$ value is greater at two sided $0.10$ significance level, so we accept the null hypothesis $[H_{0} : ρ = 0]$

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For each exercise, decide at $10 %$ significance level, whether the data provide sufficient evidence to reject the null hypothesis in favor of alternate hypothesis.
$H_{a} : ρ \neq 0$

Short Answer

Step by step solution

Step 1. Correlation Coefficient

Step 2. Hypothesis Testing

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For each exercise, decide at 10%significance level, whether the data provide sufficient evidence to reject the null hypothesis in favor of alternate hypothesis.Ha:ρ≠0

Short Answer

Step by step solution

Step 1. Correlation Coefficient

Step 2. Hypothesis Testing

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Pure Maths

Mechanics Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

For each exercise, decide at $10 %$ significance level, whether the data provide sufficient evidence to reject the null hypothesis in favor of alternate hypothesis.
$H_{a} : ρ \neq 0$