Nancy obtained a random sample of students and noticed a positive linear relationship between their ages and the amount of water (in $\mathrm{mL}$ ) they said they drank yesterday. A $95 \%$ confidence interval for the slope of the regression line was $(16.3,154.8)$.

Nancy wants to use this interval to test $\mathrm{H}_{0}: \beta=0$ vs. $\mathrm{H}_{\mathrm{a}}: \beta
eq 0$ at the $\alpha=0.05$ level of significance. Assume that all conditions for inference have been met.

Which of these is the most appropriate conclusion for this population of students?

Choose 1 answer:
A) Reject $\mathrm{H}_{0}$. Nancy can't conclude a linear relationship between age and water consumption.
(B) Fail to reject $\mathrm{H}_{0}$. Nancy can't conclude a linear relationship between age and water consumption.
(C) Reject $\mathrm{H}_{0}$. This suggests a linear relationship between age and water consumption.
(D) Fail to reject $\mathrm{H}_{0}$. This suggests a linear relationship between age and water consumption.

Question

Nancy obtained a random sample of students and noticed a positive linear relationship between their ages and the amount of water (in $\mathrm{mL}$ ) they said they drank yesterday. A $95 \%$ confidence interval for the slope of the regression line was $(16.3,154.8)$.

Nancy wants to use this interval to test $\mathrm{H}_{0}: \beta=0$ vs. $\mathrm{H}_{\mathrm{a}}: \beta 
eq 0$ at the $\alpha=0.05$ level of significance. Assume that all conditions for inference have been met.

Which of these is the most appropriate conclusion for this population of students?

Choose 1 answer:
A) Reject $\mathrm{H}_{0}$. Nancy can't conclude a linear relationship between age and water consumption.
(B) Fail to reject $\mathrm{H}_{0}$. Nancy can't conclude a linear relationship between age and water consumption.
(C) Reject $\mathrm{H}_{0}$. This suggests a linear relationship between age and water consumption.
(D) Fail to reject $\mathrm{H}_{0}$. This suggests a linear relationship between age and water consumption.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine the correct conclusion, we need to look at the confidence interval for the slope of the regression line. ‖ ‖ step 2 ⋮ The confidence interval for the slope is given as $(16.3, 154.8)$. ‖ ‖ step 3 ⋮ Since the interval does not include 0, we have evidence that the slope is not 0. ‖ ‖ step 4 ⋮ Therefore, we reject the null hypothesis $H_0: \beta = 0$. ‖ ‖ step 5 ⋮ Rejecting $H_0$ suggests that there is a statistically significant linear relationship between age and water consumption. ‖ ∻[question number] Answer∻ ***C*** ∻Key Concept∻ ⚹Confidence Interval and Hypothesis Testing⚹ ∻Explanation∻ ⚹When a confidence interval for a slope does not include 0, it indicates that there is a statistically significant linear relationship between the variables.◊What is the significance level of the hypothesis test conducted by Nancy regarding the linear relationship between age and water consumption⍭ Generate me a similar question◊⚹

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