Question

According to Professor Zarkov's correlational data, there is a statistically significant relationship between the socioeconomic level of a family and how much time the parents spend talking to their children. To say that the results of this study are "statistically significant" means that:a. the finding has no mathematical validity.b. the results are unlikely to have occurred by chance.c. there is a cause-and-effect relationship between the two variables.d. the finding can be used to generate new theories.

Answer 1

Answer:

b. the results are unlikely to have occurred by chance.

Correct when we say significant means that the difference between the hypothetical correlation coefficient of 0 and the real correlation coefficient are large enough to conclude the significant result and not just by chance.

Step-by-step explanation:

When we want to analyze of two variables present significant correlation usually we use the following system of hypothesis:

Null hypothesis: $\rho =0$

Alternative Hypothesis: $\rho \neq 0$

And when we conduct the test if we conclude that we have a significant relationship that means, we have enough evidence to conclude that the correlation coefficient is different from 0 at some significance level $\alpha$. Let's analyze one by one the possible options:

a. the finding has no mathematical validity.

False, we are conducting an hypothesis test, that procedure present validity always.

b. the results are unlikely to have occurred by chance.

Correct when we say significant means that the difference between the hypothetical correlation coefficient of 0 and the real correlation coefficient is large enough to conclude the significant result and is not just by chance.

c. there is a cause-and-effect relationship between the two variables.

False, we can't analyze causal relationships with the correlation coefficient.

d. the finding can be used to generate new theories.

That's False we can't create new theories with this result, we just can conclude that the correlation coeffcient for the population is different from 0, but nothing else.