Question

For a data set of brain volumes ​(cm3​) and IQ scores of eight males, the linear correlation coefficient is found and the​ P-value is 0.793. 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 brain volume and IQ score in males.​(Type an integer or a decimal. Do not​ round.)

Answer 1

A P-value of 0.793 indicates a high probability (79.3%) that the observed linear correlation could occur by chance under the null hypothesis; hence, there is insufficient evidence to assert a linear correlation between brain volume and IQ score.

Step-by-step explanation:

The P-value in a statistical test is the probability of obtaining a result at least as extreme as the one observed, given that the null hypothesis is true. In this case, a P-value of 0.793 is quite high and would usually be compared to a significance level (often 0.05). Since 0.793 is greater than 0.05, we conclude that there is not sufficient evidence to reject the null hypothesis. Therefore, we cannot conclude a significant linear correlation between brain volume and IQ score among males.

The P-value indicates that the probability of a linear correlation coefficient that is at least as extreme as the one observed under the null hypothesis is 79.3 percent, which is considered too high to denote a significant linear relationship. Consequently, there is insufficient evidence to assert that there is a linear correlation between the variables in question.

Answer 2

The​ P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is 0.793 which is high so there is not sufficient evidence to conclude that there is a linear correlation between brain volume and IQ score in males.

Step-by-step explanation:

We are given the following information in the question:

p-value = 0.793

Significance level = 0.05

`H_(0): \mu = \text{ The population correlation coefficient is not significantly different from 0}\\H_A: \mu = \text{ The population correlation coefficient is significantly different from 0}`

Since p value is greater than the significance value so we fail to reject the null hypothesis and accept the null hypothesis. We conclude that there is not a significant linear relationship between two variables.

Thus, we can write:

The​ P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is 0.793 which is high so there is not sufficient evidence to conclude that there is a linear correlation between brain volume and IQ score in males.