Question

Assume a researcher found that the correlation between a test she had developed and exam performance was .5 in a study of 25 students. She had previously been informed that correlations under .30 are considered unacceptable. The 95% confidence interval was [0.131, 0.747]. Can you be confident that the true correlation is at least 0.30?a. Yes you can, because the correlation coefficient is .5 (which is above .30) and falls within the boundaries of the confidence interval.b. No you cannot, because the lower boundary of the confidence interval is .131, which is less than .30, and so the true correlation could be less than .30.c. Yes you can, because the upper boundary of the confidence interval is above .30. We can be 95% confident that the true correlation will be above .30d. No you cannot, because the sample size was too small.

Answer 1

Answer: .b. No you cannot, because the lower boundary of the confidence interval is .

Explanation:

The 95% confidence interval interprets that it is 95% certain that it contains the true value of the unknown population parameter.

Given : A researcher found that the correlation between a test she had developed and exam performance was .5 in a study of 25 students.

She had previously been informed that correlations under .30 are considered unacceptable. The 95% confidence interval was [0.131, 0.747].

It means that the lower limit of the population parameter is 0.131 and the upper limit of the population parameter is 0.747.

Since, 0.131 is less than 0.30 it means that the true correlation can be less than 0.30.

So , we are not confident that the true correlation is at least 0.30.