Use the Following Information to Answer the Question -Test the Hypothesis That the Slope Is Zero (Significance Level

question 28

Multiple Choice

Use the following information to answer the question. A random sample of 30 couples who were also new home owners
were asked to report the cost of their first house and their combined age when they married. The output of a regression
analysis for predicting home cost from combined age is shown. Assume that the conditions of the linear regression model are
satisfied. $$\begin{array} { | l | l | } \hline{ \text { Regression Analysis: Combined age versus home cost } } \\\hline \text { The regression equation is } & \\\text { home cost } = 73.74 + 2122.75 \text { combined age } & \\\text { Predictor: Constant } & \text { Predictor: Combined Age } \\\text { Parameter Estimate: } 73.74 & \text { Parameter Estimate: } 2122.75 \\\text { Standard Error: } 24.655 & \text { Standard Error: } 4.814 \\\text { T-statistic: } 0.003 & \text { T-statistic: } 4.882 \\\text { p-value: } 0.998 & \text { p-value: } 0.008 \\\hline \mathrm { S } = 19837.70325 \quad \mathrm { R } - \mathrm { sq } = 0.8562890509 & \mathrm { r } = 0.9253588768 \\\hline\end{array}$$
-Test the hypothesis that the slope is zero (significance level is 0.05) , then choose the correct decision regarding the null hypothesis and the statement that correctly summarizes the conclusion.

• A) Reject \(\mathrm { H } _ { 0 }\). We don't have enough evidence to reject a slope of zero which is an indication that no linear association exists between combined age of the couple and home cost.
• B) Reject \(\mathrm { H } _ { 0 }\). There is enough evidence to reject a slope of zero which is an indication that a linear association exists between combined age of the couple and home cost.
• C) Fail to reject \(\mathrm { H } _ { 0 }\). There is enough evidence to reject a slope of zero which is an indication that a linear association exists between combined age of the couple and home cost.
• D) Fail to reject \(\mathrm { H } _ { 0 }\). We don't have enough evidence to reject a slope of zero which is an indication that no linear association exists between combined age of the couple and home cost.

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