For a data set of weights​ (pounds) and highway fuel consumption amounts​ (mpg) of eight types of​ automobile, the linear correlation coeffi

Question

For a data set of weights​ (pounds) and highway fuel consumption amounts​ (mpg) of eight types of​ automobile, the linear correlation coefficient is found and the​ P-value is 0.044. Write a statement that interprets the​ P-value and includes a conclusion about linear correlation.

The​ P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is [WHAT PERCENT] which is [LOW OR HIGH] so there [IS OR IS NOT] sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.

​(Type an integer or a decimal. Do not​ round.)

in progress 0
3 months 2021-10-19T23:34:08+00:00 1 Answer 0 views 0

The​ P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is 4.4 which is LOW so there IS sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.

Step-by-step explanation:

Hello!

Remember:

The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).

Let’s say that the significance level of this correlation test is α: 0.05

If the p-value is the probability of obtaining

you can express it as a percentage: 4.4%Is a very low probability. The decision rule using the p-value is:

p-value < α ⇒ Reject the null hypothesis

p-value ≥ α ⇒ Do not reject the null hypothesis.

The p-value is less than the significance level, the decision is to reject the null hypothesis.

In a linear correlation analysis the statement “there is no linear correlation between the two variables” is always in the null hypothesis, so if you reject it, you can conclude that there is a linear correlation between the variables.

I hope it helps!