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An article in the Journal of Sound and Vibration (Vol. 151, 1991, pp. 383–394) described a study investigating the relationship between noise exposure and hypertension. The following data are representative of those reported in the article.

a. Create a scatter diagram of y (blood pressure rise in millimeters of mercury) versus x (sound pressure level in decibels). Does a simple linear regression model seem reasonable in this situation?
b. Test the hypothesis H0: β1 = 0 using alpha = 0.05. What do you determine about the slope of the regression line?
c. What is the estimate of σ2?
d. Find the predicted mean rise in blood pressure level associated with a sound pressure level of 85 decibels.
e.Would it be reasonable to estimate the rise in blood pressure level associated with a sound pressure level of 120 decibels? Explain.
f. What proportion of total variability in blood pressure rise is accounted for by sound pressure level?

An article in the Journal of Sound and Vibration (Vol. 151, 1991, pp. 383–394) described-example-1
User Tashae
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Final answer:

The student's question involves using statistics and simple linear regression to analyze the relationship between noise exposure and blood pressure rise, suitable for college-level study in the field of statistics.

Step-by-step explanation:

The question relates to the field of statistics, specifically the use of simple linear regression to assess the relationship between noise exposure (sound pressure level in decibels) and its potential effect on hypertension (blood pressure rise in millimeters of mercury).

The elements of the question involve creating a scatter diagram, testing the hypothesis for the slope of the regression line, estimating the variance of the errors (σ^2), predicting mean blood pressure rise at a given decibel level,

assessing the appropriateness of a prediction at a sound level outside the range of the data, and determining the proportion of variability explained by the regression model.

As the question includes a hypothesis test for the slope (β1 = 0), calculating the variance of the errors (which is synonymous with the estimate of σ^2 in the context of simple linear regression), and interpreting proportions of variability, it involves advanced statistical concepts that are typically covered at the college level.

The student should be guided on how to approach each sub-question with a clear explanation of the required statistical methods and their implications on the study's findings.

User NiZa
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