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:

Interest Income

Interest income is the revenue earned from depositing funds in interest-bearing accounts, securities, or investments, where the yield comes in the form of interest payments.

Bond Premiums

The amount by which the market price of a bond exceeds its principal amount or face value, usually occurring when the market interest rate is below the coupon rate.

Interest Income

Income earned from deposit accounts or investments through the receipt of interest payments.

Fair Value

The estimated market value of an asset or liability, based on current conditions rather than historical cost.