Chapter 14: Q14.120 (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 : $p n o t = 0$ .
x 0 4 3 1 2
y 1 9 8 4 3

Short Answer

Expert verified

We don't reject Ha : $p n o t = 0$ , and state that the variables are linearly correlated.

Step by step solution

Correlation Coefficient

Sample correlation coefficient is calculated by : $r = \sum_{}^{} z x z y / (n - 1)$

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

Using excel and above formula concept, $r = 0.9325$

Hypothesis Testing

$r n o t = 0$ for sample needs to be tested using hypothesis testing, to ensure that the population correlation parameterp (rho) is non zero.

$t = r / \sqrt{(1 - r^{2}) / (n - 2)} 0.9325 / \sqrt{(1 - 0.9325) / (5 - 2)} 0.9325 / \sqrt{0.0675 / 3} 0.9325 / \sqrt{0.0225} 0.9325 / 0.15 t = 6.216$

As t calculated value is greater than t value for $10 %$ significance level ie $0.05$ each side, and p value $= 0.02$ is also lesser than p at the same significance level

So, we reject the null hypothesis H0 : $p = 0$ in favour of alternate hypothesis H1 : $p n o t = 0$ . Hence, the variables are linearly correlated.

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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 : $p n o t = 0$ .
x 0 4 3 1 2
y 1 9 8 4 3

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 :pnot=0.x04312y19843

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

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Decision Maths

Calculus

Geometry

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 : $p n o t = 0$ .
x 0 4 3 1 2
y 1 9 8 4 3