The Results of a Recent Study Regarding Smoking and Three

question 10

Essay

The results of a recent study regarding smoking and three types of illness are shown in the following table.
$\begin{array}{lrr}\text { Illness } & \text { Non-Smokers } & \text { Smokers } & \text { Totals }\\\text { Emphysema } & 50 & 150 &200\\\text { Heart problem } & 50 & 150&200 \\\text { Cancer } & 100 & 500&600\\ \text { Totals }&200&800&1000\end{array}$ 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 and determine the test statistic.
c. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test
d. What do you conclude?

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Definitions:

Conditional Distributions

The probability distribution of a random variable contingent upon the realization of another variable.

Contingency Table

A contingency table, also known as a cross-tabulation or crosstab, is a table that displays the frequency distribution of variables to analyze the relationship between two or more categorical variables.

Beer

An alcoholic beverage made from fermented grains, typically barley, and flavored with hops.

Wine

An alcoholic beverage made from fermented grapes or other fruits.