Chapter 14: Q14.122 (page 585)

For each exercise, decide at 10% significance level, whether the data provide sufficient evidence to reject the null hypothesis in favour of alternate hypothesis
Ha : $p \neq 0$

Short Answer

Expert verified

$H a : p \neq 0$ is rejected. The variables are not linearly correlated.

Step by step solution

Correlation Coefficient

Sample correlation coefficient r 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 $z y_{n}$

Using excel and above formula concept, $r = - 0.7206$

Hypothesis Testing

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

$t = r / \sqrt{(1 - r^{2}) / (n - 2)} - 0.7206 / \sqrt{0.4807 / 2} - 0.7206 / 0.4903 t = - 1.469$

As t calculated value at 0.10 significance level is more that, and p value at the same significance level $= 0.2794$ is more

So, we accept the null hypothesis in $p = 0$ , and reject the null hypothesis.

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For each exercise, decide at 10% significance level, whether the data provide sufficient evidence to reject the null hypothesis in favour of alternate hypothesis
Ha : $p \neq 0$

Short Answer

Step by step solution

Correlation Coefficient

Hypothesis Testing

One App. One Place for Learning.

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For each exercise, decide at 10% significance level, whether the data provide sufficient evidence to reject the null hypothesis in favour of alternate hypothesisHa :p≠0

Short Answer

Step by step solution

Correlation Coefficient

Hypothesis Testing

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Discrete Mathematics

Logic and Functions

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 favour of alternate hypothesis
Ha : $p \neq 0$