# Question: A researcher believes that the stock market performance and

Question:
A researcher believes that the stock market performance and the property market performance in Singapore are associated. Describe one (1) statistical approach the researcher would implement to determine the association between the performances of these two markets. Explain their association and the factors that affect their association.
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Given information:
Given that the researcher believes that the stock market performance and the property market performance in Singapore are associated.
Correlation:
Correlation analysis is used to measure the strength of the association between variables. In other words, it can be said that correlation describes the linear associations between quantitative variables.
The two variables of interest are X = Stock market performance and Y = Property market performance.
The significance of association between the variables X and Y can be determined by testing the significance of correlation.
Test procedure:
The test procedure is as given below:
In order to test the hypothesis regarding the direction of relation between a paired set of n observations (xi, yi), a significance test for correlation is appropriate. Hence, the appropriate statistics is correlation.
Thus, the sampling distribution used in the given scenario is “Student’s t”.
Denote r as the sample correlation coefficient and ρ as the population correlation coefficient.
The null and alternate hypotheses are stated below:
Null hypothesis ${H}_{0}:\phantom{\rule{0ex}{0ex}}{H}_{0}:\rho =0$
That is, there exists no significant relationship between the variable’s stock market performance and property market performance.
Alternative hypothesis${H}_{1}:\phantom{\rule{0ex}{0ex}}{H}_{1}:\rho \ne 0$
That is, there exists a significant relationship between the variable’s stock market performance and property market performance.
Test statistic:
The test statistic is obtained as given below:
$t=\frac{r\sqrt{n-2}}{\sqrt{1-{r}^{2}}}\phantom{\rule{0ex}{0ex}}df=n-2$
Decision rule:
Denote t as test statistic value and $±{t}_{\frac{\alpha }{2}}$ are the critical values.
Decision rule based on critical approach: