Hypothesis testing

#1
Here I am again....Thank you so much for helping me out yesterday. I am lost when it comes to Hypothesis testing....What do you think about this question since I have no clue?

A nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but we can nonetheless examine the relationship between scores on such tests and performance in college.

We have chosen a random sample of 95 students just finishing their first year of college, and for each student we've recorded her score on one such standardized test and her grade point average for her first year in college. The sample correlation coefficient r for our data is approximately .27. Based on these sample results, test for a significant linear relationship between the two variables score on this standardized test and first-year college grade point average by doing a hypothesis test regarding the population correlation coefficient . (Assume that the two variables have a bivariate normal distribution.) Use the level of significance 0.5, and perform a two-tailed test. Then fill in the table below.

Find

Null Hypothesis
Alternate hypothesis
The type of test statistic
The value of test statistic
The P- value
Based on the samples results can we conclude(using the .5 significance level) that there is a significant linear relationship between score and standarized test and first year college GPA? yes or no....


Thanks so much.....
 

JohnM

TS Contributor
#2
Here you are testing whether "r" (the correlation coefficient) is significantly different from 0

--> in other words, is there a real correlation in the population between test scores and college performance, or is the correlation we see in our sample just a random occurrence?

the correlation coefficient r usually follows a t distribution - do you have access to any class/lecture notes that discuss how to test the significance of a corelation coefficient?