Listed below are the numbers of words spoken in a day by each member of eight different randomly selected couples. Complete parts (a) and (b) below.
\begin{tabular}{lcccccccc}
\hline Male & 15,293 & 25,431 & 1365 & 7570 & 19,378 & 15,773 & 13,703 & 25,084 \\
\hline Female & 25,290 & 12,916 & 18,352 & 18,492 & 13,467 & 16,804 & 16,406 & 19,012 \\
\hline
\end{tabular}
Identify the P-value.
P-value $=0.283$ (Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
Since the P-value is greater than the significance level, fail to reject the null hypothesis. There is not sufficient evidence to support the claim that males speak fewer words in a day than females.
b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)?
The confidence interval is $\square$ word(s) $< \mu_{d}< \square$ word(s).
(Round to the nearest integer as needed.)
Answer
Final Answer: The confidence interval is \(\boxed{-9111}\) word(s) \(<\mu_{d}<\boxed{4826}\) word(s).
Step 1 ：Given the number of words spoken by males and females, we first calculate the mean difference between the two sets of data. The mean difference is -2142.75 words.
Step 2 ：We then calculate the standard deviation of the differences, which is 10055.99 words.
Step 3 ：Next, we calculate the standard error of the mean difference, which is 3555.33 words.
Step 4 ：We use a z-score of 1.96 for a 95% confidence level.
Step 5 ：We calculate the lower and upper bounds of the confidence interval by subtracting and adding the product of the z-score and the standard error from the mean difference, respectively. The lower bound is -9111 words and the upper bound is 4825.57 words.
Step 6 ：Rounding to the nearest integer, the upper bound becomes 4826 words.
Step 7 ：Final Answer: The confidence interval is \(\boxed{-9111}\) word(s) \(<\mu_{d}<\boxed{4826}\) word(s).
