Question

Question 252 pts

A student has just run her inferential statistics and found that the results were statistically significant at the 5% level. When she rushes excitedly to her professor with the news, what is the professor likely to say?

Group of answer choices

“There is more than a 5% chance that the results have practical significance.”

“Fantastic, you have found that the independent variable and the dependent variable are correlated beyond a chance level.”

“Congratulations, the results indicate that the dependent variable influenced the independent variable.”

“There is a 5% chance that the results were due to chance factors.”

Answer 1

Suppose, the student was asked to test, whether the independent variable and the dependent variable are correlated.On analysing the data, she must have obtained the p-value of the test to be less than the 5% signifiance level and thus found the result to be statistically significant at the 5% level - indicates a 5% risk of concluding that a a significant correlation exists when there is no actual one.

By definition of P-value,

The P stands for probability and measures how likely it is that any observed correlation between the independent variable and the dependent variable is purely due to chance;i.e. no actual correlation exists.

Being a probability, P can take any value between 0 and 1. Values close to 0 indicate that the observed correlation is unlikely to be due to chance, whereas a P value close to 1 suggests that there is no relationship between the two cariables other than due to chance.

Here, the student must have obtained a p-value < fixed error rate (significance level), a value more closer to zero, which as mentioned above, indicate that the observed correlation is unlikely to be due to chance.

Hence, the correct option would be:

“Fantastic, you have found that the independent variable and the dependent variable are correlated beyond a chance level.”