Questions: The accompanying data are measured body temperatures of adults at 12 AM on a certain day. Use the Wilcoxon signed-ranks test to test the claim that the median is equal to 98.6°F. Use a 0.01 significance level. Determine the null and alternative hypotheses. H0: The median body temperature is equal to 98.6°F H1: The median body temperature is not equal to 98.6°F (Type integers or decimals. Do not round.) Determine the P-value. The P-value is (Round to three decimal places as needed.) Determine the proper conclusion. Reject or Do not reject H0. There is sufficient or insufficient evidence at the 0.01 significance level to warrant rejection of 98.6°F. Body Temperature Data 98.1 97.7 98.7 97.9 98.7 98.9 97.5 98.5 98.5 98.7 98.1 98.3 97.9 98.1 97.1 97.3 98.1 98.2 98.3 98.4 98.6 99.1 97.9 96.9 97.4 97.2 98.0 97.9 98.9 97.7 97.5 98.1 97.5 98.1 98.5 98.7 98.3 97.1 98.5 99.1 98.1 99.5 97.9 98.1 99.3 99.1 97.8 98.1 98.1 98.7 98.2 98.6 97.3 98.6 99.3 98.2 98.8 98.7 98.5 97.9 99.2 97.3 97.7 97.8 98.9 98.5 98.5 99.4 97.7 98.6 99.4 97.7 98.5 97.6 98.4 97.8 97.0 98.3 98.7 97.5 96.8 97.0 98.3 98.3 98.5 97.1 97.3 98.5 97.5 96.7 98.1 97.3 97.9

The accompanying data are measured body temperatures of adults at 12 AM on a certain day. Use the Wilcoxon signed-ranks test to test the claim that the median is equal to 98.6°F. Use a 0.01 significance level. Determine the null and alternative hypotheses. H0: The median body temperature is equal to 98.6°F H1: The median body temperature is not equal to 98.6°F (Type integers or decimals. Do not round.) Determine the P-value. The P-value is (Round to three decimal places as needed.) Determine the proper conclusion. Reject or Do not reject H0. There is sufficient or insufficient evidence at the 0.01 significance level to warrant rejection of 98.6°F. Body Temperature Data 98.1 97.7 98.7 97.9 98.7 98.9 97.5 98.5 98.5 98.7 98.1 98.3 97.9 98.1 97.1 97.3 98.1 98.2 98.3 98.4 98.6 99.1 97.9 96.9 97.4 97.2 98.0 97.9 98.9 97.7 97.5 98.1 97.5 98.1 98.5 98.7 98.3 97.1 98.5 99.1 98.1 99.5 97.9 98.1 99.3 99.1 97.8 98.1 98.1 98.7 98.2 98.6 97.3 98.6 99.3 98.2 98.8 98.7 98.5 97.9 99.2 97.3 97.7 97.8 98.9 98.5 98.5 99.4 97.7 98.6 99.4 97.7 98.5 97.6 98.4 97.8 97.0 98.3 98.7 97.5 96.8 97.0 98.3 98.3 98.5 97.1 97.3 98.5 97.5 96.7 98.1 97.3 97.9
Transcript text: The accompanying data are measured body temperatures of adults at 12 AM on a certain day. Use the Wilcoxon signed-ranks test to test the claim that the median is equal to $98.6^{\circ} \mathrm{F}$. Use a 0.01 significance level. Determine the null and alternative hypotheses. $\mathrm{H}_{0}$ : The median body temperature is $\square$ $\square^{\circ}$ $\mathrm{H}_{1}$ : The median body temperature is $\square$ $\square^{\circ}$ (Type integers or decimals. Do not round.) Determine the P -value. The P -value is $\square$ (Round to three decimal places as needed.) Determine the proper conclusion. $\square$ $\mathrm{H}_{0}$. There is $\square$ evidence at the 0.01 significance level to w. $98.6^{\circ} \mathrm{F}$. Body Temperature Data \begin{tabular}{|llllll|} \hline 98.1 & 97.7 & 98.7 & 97.9 & 98.7 \\ 98.9 & 97.5 & 98.5 & 98.5 & 98.7 \\ 98.1 & 98.3 & 97.9 & 98.1 & 97.1 \\ 97.3 & 98.1 & 98.2 & 98.3 & 98.4 \\ 98.6 & 99.1 & 97.9 & 96.9 & 97.4 \\ 97.2 & 98.0 & 97.9 & 98.9 & 97.7 \\ 97.5 & 98.1 & 97.5 & 98.1 & 98.5 \\ 98.7 & 98.3 & 97.1 & 98.5 & 99.1 \\ 98.1 & 99.5 & 97.9 & 98.1 & 99.3 \\ 99.1 & 97.8 & 98.1 & 98.1 & 98.7 \\ 98.2 & 98.6 & 97.3 & 98.6 & 99.3 \\ 98.2 & 98.8 & 98.7 & 98.5 & 97.9 \\ 99.2 & 97.3 & 97.7 & 97.8 & 98.9 \\ 98.5 & 98.5 & 99.4 & 97.7 & 98.6 \\ 99.4 & 97.7 & 98.5 & 97.6 & 98.4 \\ 97.8 & 97.0 & 98.3 & 98.7 & 97.5 \\ 96.8 & 97.0 & 98.3 & 98.3 & 98.5 \\ 97.1 & 97.3 & 98.5 & 97.5 & 96.7 \\ 98.1 & 97.3 & 97.9 & & \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Define Hypotheses

We are testing the claim that the median body temperature is equal to \( 98.6^{\circ} \mathrm{F} \).

  • Null Hypothesis (\( H_0 \)): The median body temperature is \( 98.6^{\circ} \mathrm{F} \).
  • Alternative Hypothesis (\( H_1 \)): The median body temperature is not \( 98.6^{\circ} \mathrm{F} \).
Step 2: Perform the Wilcoxon Signed-Ranks Test

We calculate the differences between each body temperature measurement and the hypothesized median:

\[ \text{Differences} = \text{Body Temperatures} - 98.6 \]

The Wilcoxon signed-ranks test yields the following results:

  • Test Statistic: \( W = 672.5 \)
  • P-value: \( p = 0.000 \)
Step 3: Compare P-value with Significance Level

We set the significance level \( \alpha = 0.01 \).

Since \( p < \alpha \) (i.e., \( 0.000 < 0.01 \)), we reject the null hypothesis.

Step 4: Conclusion

There is sufficient evidence at the \( 0.01 \) significance level to conclude that the median body temperature is not \( 98.6^{\circ} \mathrm{F} \).

Final Answer

\[ \boxed{H_0 \text{ is rejected. There is sufficient evidence to conclude that the median body temperature is not } 98.6^{\circ} \mathrm{F}.} \]

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