An investigation of the relationship between years of formal education and IQ that was conducted with a sample size of 100 found a statistically significant correlation of .25.Another investigation of the same relationship had the same r value based on a sample size of 10,but it was not statistically significant.Why might this be?
A)a sample size of 100 has too much sampling error
B)a sample size of 10 is more likely to produce a Type I error
C)as sample size increases so does the power of the statistic
D)the standard error was larger in the sample where N = 100

Question

Quizplus · Accepted Answer

As sample size increases, the power of the statistic increases. This means that it becomes more likely to correctly reject the null hypothesis when there is a true relationship between the variables. Therefore, with a larger sample size, the correlation in the first investigation was more likely to be statistically significant, whereas with a smaller sample size, the second investigation had lower power to detect a significant relationship.

An Investigation of the Relationship Between Years of Formal Education