Final answer:
The conclusion of the hypothesis test for the significance of the correlation coefficient depends on comparing the absolute value of the test statistic with the critical value. With a typo in the test statistic value provided, the exact conclusion cannot be determined. Generally, a p-value smaller than the significance level would lead to rejecting the null hypothesis.
Step-by-step explanation:
The student asks about hypothesis testing for the significance of the correlation coefficient between the returns of two stocks, X and Y. Given a test statistic value 't28-231' and a critical value 'to .025, 28-2048', it seems there's a typo in the provided statistic value. Assuming the test statistic follows a t-distribution with 28 degrees of freedom, the conclusion depends on comparing the absolute value of the test statistic with the critical value from the t-distribution table.
If the calculated test statistic is larger than the critical value (in absolute terms), we reject the null hypothesis. This means we have sufficient evidence to conclude there is a significant linear relationship between the rates of return for stock X and stock Y. However, if the test statistic is smaller than the critical value, we fail to reject the null hypothesis, indicating we do not have evidence of a significant correlation.
Since there is a typo in the value of the test statistic provided, the conclusion cannot be accurately determined from the information given. In general, if a p-value is provided (like 0.026) which is less than the significance level (like 0.05), the conclusion would be to reject the null hypothesis and conclude that a significant linear relationship exists.