Use the Wilcoxon Signed-Rank Test to Perform the Required Hypothesis $$\begin{array} { l l l l l l } 4.7 & 4.5 & 5.2 & 5.1 & 4.0 & 5.4 \\ 4.1 & 3.7 & 3.2 & 4.3 & 4.4 & 3.5 \end{array}$$

Essay

Use the Wilcoxon signed-rank test to perform the required hypothesis test. Be sure to state the hypotheses and thesignificance level, to obtain the critical value(s), to compute the value of the test statistic, and to state your conclusion.
-The forced vital capacity (FVC)is often used by physicians to assess a person's ability to move air in and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. For adult males, the average FVC is 5.0 liters. A researcher wants to perform a hypothesis test to determine whether the average forced vital capacity for women differs from this value. A random sample of 12 women yielded the following values for FVC, in liters.

$$\begin{array} { l l l l l l } 4.7 & 4.5 & 5.2 & 5.1 & 4.0 & 5.4 \\ 4.1 & 3.7 & 3.2 & 4.3 & 4.4 & 3.5 \end{array}$$ At the 1% significance level, do the data provide sufficient evidence to conclude that the mean forced vital capacity for women differs from the mean value for men of 5.0 liters?