posted by Ethel on .
b. The correlation between the number correct on a math test and the time it takes to complete the test is -.45. Test whether this correlation is significant for 80 children at the .05 level of significance. Choose either a one-or two-tailed test and justify your choice.
To find if there is a statistically significant linear relationship between the number correct on a math test and the time it takes to complete the test, use N-2 for degrees of freedom at the .05 significance level for a one-tailed test or a two-tailed test. Use a table for critical or cutoff values for a Pearson r. Compare the value from the table to the test statistic stated in the problem. If the test statistic exceeds the critical value from the table (negative direction for a one-tailed in this case or either direction for a two-tailed), the null will be rejected. There will be a linear relationship in the population and the test will be statistically significant. If the test statistic does not exceed the critical value from the table, then the null will not be rejected and you cannot conclude a linear relationship in the population.