Question

A researcher is interested in the correlation between an IQ test and scores on a particular 8th grade achievement test. The students's scores are assumed to be normal and the scale of this test has been converted to the same scale as the IQ test. The following data is for a sample of 30 eighth graders:

IQ Test Mean: 109 IQ Test S.D: 18

Achievement Test Mean: 104 Achievement Test S.D:. 22

Correlation of Test Scores: r=0.47

a) what does the magnitude of the correlation suggest about the relationship between students' IQ scores and their outcomes on the achievement test?

b) Some researchers claim that students always do better on this particular achievement test than their IQ would predict. What kind of test statistic would you use to test this hypothesis? Be sure to specify the specific test statistic and directionality of the test, if appropriate. Explain the reasoning behind your choice, BUT DO NOT CALCULATE the test statistic!

Answer 1

(A) We know that any correlation with magnitude in the range of 0.40 to 0.60, is termed as moderate correlation. In this case, the magnitude of correlation coefficient is 0.47, which is less than 0.50. So, this magnitude is suggesting that the correlation is moderate, not strong.

(B) Sample size is 30 and population variances are unknown, so it is better to use t test for mean difference to test the hypothesis because when sample size is small and population variance is unknown, then we t test is more useful and accurate as compared to z test. It is two tailed hypothesis because the researcher is interested in testing whether there is any correlation between the IQ test and scores on a particular 8th grade achievement test.