For a sample of 66 months, the correlation between the...

Name: Problem 72, Chapter 11: Statistics for Business and Economics: Global Edition
Uploaded: 2022-02-16T11:22:31-08:00
Duration: 31 s
Channel: Christopher Stanley
Description: For a sample of 66 months, the correlation between the returns on Canadian and Singapore 10-year bonds was found to be 0.293 . Test the null hypothesis that the population correlation is 0 against the alternative that it is positive.

For a sample of 66 months, the correlation between the returns on Canadian and Singapore 10-year bonds was found to be 0.293 . Test the null hypothesis that the population correlation is 0 against the alternative that it is positive.

Key Concepts

One-tailed Test

A one-tailed test is used when the alternative hypothesis specifies a directional effect (for example, testing whether the correlation is positive). This approach focuses on detecting an effect in one predetermined direction, which can provide more power to detect an effect when the direction of the effect is known a priori.

Significance Test for Correlation

A significance test for the correlation coefficient assesses whether the observed sample correlation is statistically significantly different from zero, indicating a non-random linear association in the population. This is often done by converting the sample correlation into a test statistic and comparing it against critical values from a t-distribution.

T-statistic for Correlation

The t-statistic for testing the significance of a correlation coefficient is computed using the formula t = r?((n-2)/(1-r²)), where r is the sample correlation and n is the sample size. This transformation allows the correlation to be tested against the t-distribution with n-2 degrees of freedom under the null hypothesis that the population correlation is zero.

Hypothesis Testing

Hypothesis testing is a systematic method used to determine if there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. It involves establishing a null hypothesis (a baseline assumption) and an alternative hypothesis, then using statistical methods to decide whether to reject the null hypothesis in favor of the alternative.

Correlation Coefficient

The correlation coefficient is a statistical measure that quantifies the degree to which two variables have a linear relationship. Its value ranges from -1 to 1, with values near 1 or -1 indicating strong positive or negative linear relationships, respectively, and a value of zero implying no linear association.

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