Math  /  Data & Statistics

QuestionQuestion 9 of 10 (1 point) I Question Attempt 3 of Unlimited
Fast reactions: In a study of reaction times, the time to respond to a visual stimulus (x)(x) and the time to respond to an auditory stimulus ( yy ) were recorded for each of 7 subjects. Times were measured in thousandths of a second. The results are presented in the following table. \begin{tabular}{cc} \hline Visual & Auditory \\ \hline 161 & 159 \\ 176 & 163 \\ 178 & 201 \\ 188 & 193 \\ 201 & 197 \\ 203 & 206 \\ 211 & 189 \\ \hline \end{tabular} Send data to Excel
The least-squares regression line y^=b0+b1x=51.2341+0.7203x\hat{y}=b_{0}+b_{1} x=51.2341+0.7203 x and Σ(xxˉ)2=1895.4286\Sigma(x-\bar{x})^{2}=1895.4286 are known for this data. Construct a 95%95 \% confidence interval for the slope. Round the answers to at least four decimal places.
The 95%95 \% confidence interval is \square <β1<<\beta_{1}< \square 1. Save For Later Submit Assig

Studdy Solution
Construct the confidence interval for the slope β1\beta_1 using:
b1±tSEb1b_1 \pm t^* \cdot SE_{b_1}
Substitute the values for b1b_1, tt^*, and SEb1SE_{b_1}.
The 95% confidence interval for the slope β1\beta_1 is:
Lower bound<β1<Upper bound\boxed{\text{Lower bound}} < \beta_1 < \boxed{\text{Upper bound}}

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