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

question 19

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?

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Definitions:

Internal Validity

The extent to which a study can demonstrate a causal relationship between variables, minimizing the influence of external factors.

Independent Variable

A variable that is manipulated or changed in an experiment to observe its effects on a dependent variable.

Dependent Variable

In experimental research, the variable that is observed and measured to determine the effect of the independent variable, reflecting outcomes or changes.

External Validity

The extent to which the results of a study can be generalized to other situations and to other people.