Decide, at the Given Significance Level, Whether the Data Provide

question 36

Essay

Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful forpredicting y.
-Applicants for a particular job, which involves extensive travel in Spanish speaking countries, must take a proficiency test in Spanish. The sample data below were obtained in a study of the relationship between the numbers of years applicants have studied Spanish (x)and their score on the test (y). $$\begin{array}{l} \begin{array} { c c c c c c c c c c c } \hline \mathrm { x } & 3 & 4 & 4 & 2 & 5 & 3 & 4 & 5 & 3 & 2 \\ \hline \mathrm { y } & 57 & 78 & 72 & 58 & 89 & 63 & 73 & 84 & 75 & 48 \\ \hline \end{array}\\ \hat { y } = 31.55 + 10.90 x \end{array}$$ The standard error of the estimate is approximately 5.651. At the 5% level of significance, do the data provide sufficient evidence to conclude that the slope of the population regression line is not 0 and hence that number of years of study is useful as a predictor of score on the test?

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Definitions:

General Adaptation Syndrome

A three-stage physiological response to stress that consists of alarm, resistance, and exhaustion phases, as proposed by Hans Selye.

Poisonous Snake

Describes a snake capable of delivering venom through a bite, which can be harmful or lethal to humans and other animals.

Alarm Reaction

The initial response of the body to a perceived threat, part of the stress response, involving physiological changes such as increased heart rate and adrenaline release.

Coping Strategy

Techniques or methods employed by individuals to manage and navigate through emotional stress or problematic situations.