Over the past 30 years, the sample standard deviations of the rates of return fo
ID: 3228066 • Letter: O
Question
Over the past 30 years, the sample standard deviations of the rates of return for stock X and Stock Y were 0.30 and 0.15. respectively. The sample covariance between the returns of X and Y is 0.0096. The correlation of the rates of return between X and Y is closer to: A. 0.40 B. 0.36 C. 0.24 D. 0.21 The following scatterplot implies that the relationship between the two variables x and y is: A. Strong and positive. B. Weak and negative. C. No relationship. D. Strong and negative. Over the past 30 years, the sample standard deviations of the rates of return for stock X and Stock Y were 0.20 and 0.12, respectively. The sample covariance between the returns of X and Y is 0.0096. When testing whether the correlation coefficient differs from zero, the value of the test statistic is r_ = 2.31. At the 5% significance level, the critical value is r_ = 2.048. The conclusion to the hypothesis test is to: A. Do not reject H_0: we can conclude that the correlation coefficient differs from zero. B. Do not reject H_0: we cannot conclude that the correlation coefficient differs from zero. C. Reject H_0: we cannot conclude that the correlation coefficient differs from zero. D. Reject H_0: we can conclude that the correlation coefficient differs from zero.Explanation / Answer
31) The formula for correlation is as below:
cor(X,Y)= cov(X,Y)/(sd(X)*sd(Y))
= 0.0096/(0.30 * 0.15) = 0.0096/0.045 = 0.2133333 = 0.21 approx.
So option D is correct.
32) From the graph, we can clearly see that as x increases, the value of y also increases. So this indicates a postive correlation. So option A is correct. Correlation is strong and positive.
33) It is given that the test statistic is 2.31. And at 5% significance level, the critical value is 2.048.
So as the test statistic is greater than the critical value we can reject the null hypothesis. That means that correlation coefficient differs from zero. So option D is correct.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.