Question

Math

Posted 3 months ago

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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. $\mathrm{H}_{\mathrm{a}}: \beta \neq 0$ 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.
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Answer from Sia

Posted 3 months ago

Solution by Steps

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.

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