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:

Motivations

The driving forces behind human actions and behaviors, which can stem from psychological, social, or physiological needs.

Actions

The process of doing something, typically to achieve an aim or handle a problem.

Client-centered Therapy

A psychotherapeutic approach developed by Carl Rogers that emphasizes the therapist's empathy and the client's self-worth.

Insight

The understanding of a specific cause and effect within a specific context.