The Results of a Recent Study Regarding Smoking and Three

question 15

Essay

The results of a recent study regarding smoking and three types of illness are shown in the following table.
$$\begin{array} { l r r r } \text { Illness } & \text { Nom-Smokers } & \text { Smokers } & \text { Totals } \\\text { Emphysema } & 20 & 60 & 80 \\\text { Heart problem } & 70 & 80 & 150 \\\text { Cancer } & 30 & 40 & 70 \\\text { Totals } & 120 & 180 & 300\end{array}$$ We are interested in determining whether or not illness is independent of smoking.
a. State the null and alternative hypotheses to be tested.
b. Show the contingency table of the expected frequencies.
c. Compute the test statistic.
d. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude?
e. Determine the p-value and perform the test.

Calculate test statistics and critical values for the Wilcoxon Signed-Rank test.

Conduct hypothesis testing using the Wilcoxon Signed-Rank test and conclude based on the test results.

Recognize the conditions under which the Wilcoxon Signed-Rank test is appropriate to use.

Understand the treatment of tied values in the Wilcoxon Signed-Rank test.

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Definitions:

Expected Return

This represents the mean of the probability distribution of possible returns for a security or portfolio.

Complete Portfolio

A complete portfolio represents a combination of risk-free assets and risky assets, designed to balance potential returns with the investor's risk tolerance.

Risk-Free Asset

An investment that is assumed to have no risk of financial loss, often represented by government bonds or treasury bills.

Risky Asset

An investment that holds a certain degree of risk, possibly leading to loss, such as stocks or commodities.