Question

Researchers surveyed 1,000 randomly selected adults in the U.S. A statistically significant, strong positive correlation was found between income level and the number of containers of recycling they typically collect in a week.

1. Please select the best interpretation of this result.
Group of answer choices:
O This result indicates that earning more money influences people to recycle more than people who earn less money.
O We can not conclude whether earning more money causes more recycling among U.S. adults because this type of design does not allow us to infer causation.
O This sample is too small to draw any conclusions about the relationship between income level and amount of recycling for adults in the U.S.

Answer 1

Null hypothesis:
`\rho =0`

Alternative hypothesis:
`\rho \\eq 0`

The statistic to check the hypothesis is given by:

`t=(r √(n-2))/(√(1-r^2))`

And is distributed with n-2 degreed of freedom. df=n-2[/tex]

For this case we got a significant result that means that the real correlation coefficient is different from 0 . And for this case the best interpretation would be:

This result indicates that earning more money influences people to recycle more than people who earn less money

Explanation:

The correlation coeffcient is given by this formula:

`r=(n(\sum xy)-(\sum x)(\sum y))/(√([n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]))`

For this case we know that this value of r is positive and represent a string correlation between income level and the number of containers of recycling

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis:
`\rho =0`

Alternative hypothesis:
`\rho \\eq 0`

The statistic to check the hypothesis is given by:

`t=(r √(n-2))/(√(1-r^2))`

And is distributed with n-2 degreed of freedom. df=n-2[/tex]

For this case we got a significant result that means that the real correlation coefficient is different from 0 . And for this case the best interpretation would be:

This result indicates that earning more money influences people to recycle more than people who earn less money