vork 14 sections 11.2 and 11.3
Question 2, 11.2.3-P
HW Score: \( 70 \%, 7 \) of 10 points
Pait 78
Points: 0 of 1
Assume that the differences for the given data are normally distributed. Complete parts (a) through (d).
Click here to view the sample data. Click here to view the table of critical t-values.
(b) Compute \( \bar{d} \) and \( \mathrm{s}_{\mathrm{d}} \).
\( \bar{d}=-1.586 \) (Round to three decimal places as needed.)
\( \mathbf{S}_{d}=1.849 \) (Round to three decimal places as needed.)
(c) Test if \( \mu_{d}<0 \) at the \( \alpha=0.05 \) level of significance.
Determine the null and alternative hypotheses. Choose the correct answer below.
A. \( H_{0}: \mu_{d}=0 \)
B. \( H_{0}: \mu_{d}<0 \)
\[
H_{1}: \mu_{d}<0
\]
\[
\mathrm{H}_{1}: \mu_{\mathrm{d}}=0
\]
c. \( \mathrm{H}_{0}: \mu_{\mathrm{d}}<0 \)
D. \( H_{0}: \mu_{d}>0 \)
\[
H_{1}: \mu_{d}>0
\]
\[
H_{1}: \mu_{d}<0
\]
Determine the test statistic.
The test statistic is -2.27 .
(Round to two decimal places as needed.)
Determine the range of the \( P \)-value.
The P-value is between 0.025 and 0.05 .
Determine the proper conclusion.
Do not reject the null hypothesis. There is insufficient evidence that \( \mu_{d}=0 \) at the \( \alpha=0.05 \) level of significance.
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