A recent study of 15 shoppers showed that the correlation between the time spent in the store and the dollars spent was 0.235. Using a significance level equal to 0.05, which of the following is true?
A) The null hypothesis that the population mean is equal to zero should be rejected and we should conclude that the true correlation is not equal to zero.
B) Based on the sample data there is not enough evidence to conclude that the true correlation is different from zero.
C) The sample correlation coefficient could be zero since the test statistic does not fall in the rejection region.
D) The null hypothesis should be rejected because the test statistic exceeds the critical value.

Question

Quizplus · Accepted Answer

With a correlation coefficient of 0.235, especially in a small sample size of 15, it's likely that there isn't enough evidence to reject the null hypothesis that the true population correlation is zero. This is because a correlation of 0.235 is relatively low, indicating a weak linear relationship, and without knowing the exact critical value or conducting a specific statistical test (like Pearson's r test), we cannot definitively say the correlation is significantly different from zero at the 0.05 significance level.

A Recent Study of 15 Shoppers Showed That the Correlation