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

question 20

Multiple Choice

Use the following information to answer the question. A random sample of 30 married couples were asked to report the
height of their spouse and the height of their biological parent of the same gender as their spouse. The output of a regression
analysis for predicting spouse height from parent height is shown. Assume that the conditions of the linear regression model
are satisfied. $$\begin{array} { | l | l | } \hline { \text { Regression Analysis: Spouse versus Parent } } \\\hline \text { The regression equation is } & \\\text { spouse } = 48.40 + 0.25 \text { parent } & \\\text { Predictor: Constant } & \text { Predictor: Parent } \\\text { Parameter Estimate: } 48.398 & \text { Parameter Estimate: } 0.247 \\\text { Standard Error: } 39.695 & \text { Standard Error: } 0.566 \\\text { T-statistic: } 1.219 & \text { T-statistic: } 0.437 \\\text { p-value: } 0.277 & \text { p-value: } 0.680 \\\hline \text { S=7.794899045 } \quad \text { R-sq } = 0.036858791 \quad \mathrm { r } = 0.1919864344 \\\hline\end{array}$$
-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) 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 parent height and spouse height.
• B) 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 parent height and spouse height.
• C) Reject \(\mathrm { H } _ { 0 }\). There is enough evidence to reject a slope of zero which is an indication that a linear association exists between parent height and spouse height.
• 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 parent height and spouse height.

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