Letx X1xn Be The Blood Pressure Measured In Mm Hg And Lety Y ✓ Solved

Letx X1xn Be The Blood Pressure Measured Inmmhg And Lety Y

Let X = ( X1, ..., Xn ) be the blood pressure (measured in mmHg) and Y = ( Y1, ..., Yn ) be the cortisol level (measured in mcg/dL) recorded for n=79 patients recruited for a study in a hospital. Xi and Yi are measurements for the same patient. The question asks: Which statistical test is most appropriate to gather evidence towards the hypothesis that blood pressure is associated with cortisol level? The options are:

  • A) The two-sample paired t-test with the null hypothesis that the means of X and Y differ.
  • B) The test with the null hypothesis that the Pearson correlation coefficient between X and Y is zero.
  • C) The test with the null hypothesis that the regression coefficient is zero in a linear regression with response variable X (blood pressure) and explanatory variable Y (cortisol level).

Reasoning: To assess whether there is an association between blood pressure and cortisol level, the most suitable approach is to examine the correlation or dependence between the two variables. The paired t-test (option A) compares means of two measurements, which are in different units and are not necessarily meant to be means of the same variable. Therefore, it is not appropriate here for testing association. Option C involves modeling the relationship through regression, which is appropriate, but typically, we start with testing correlation. Option B offers a direct test of the null hypothesis that the correlation coefficient is zero, which indicates no association. The Pearson correlation test is standard for examining linear association between two continuous variables measured on the same subjects. Hence, option B provides the most straightforward and appropriate test to evaluate whether blood pressure and cortisol levels are associated.

Sample Paper For Above instruction

In investigating the potential association between blood pressure and cortisol levels, selecting the appropriate statistical test is crucial. Given that both variables are measured on the same patients, and the objective is to determine whether there is evidence of an association, the Pearson correlation coefficient presents a suitable measure. The null hypothesis in this context is that there is no linear association, i.e., the correlation coefficient is zero.

Traditional methods to assess the relationship include parametric correlation tests, such as the Pearson correlation test. This test evaluates whether the observed correlation coefficient significantly deviates from zero, indicating a potential linear relationship. The null hypothesis (H0) states that the true correlation is zero, implying no linear association, whereas the alternative suggests some degree of association.

Other options, such as the paired t-test, compare means of two variables—appropriate when measuring the same variable under different conditions or groups. However, for assessing association or dependence between two variables measured on the same subjects, correlation analysis is more direct. Linear regression modeling can also be used to explore associations; however, it is often subsequent to correlation testing, which provides a simpler initial assessment.

In conclusion, the most appropriate statistical test in this setting is the test for zero Pearson correlation coefficient between blood pressure and cortisol level (option B). It effectively captures the linear relationship and provides straightforward interpretation. If significant evidence is found to reject the null hypothesis, it hints that blood pressure and cortisol levels are associated, warranting further modeling and investigation.

References

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