Test the Indicated Claim About the Means of Two Populations

question 20

Essay

Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. $$\begin{array} { | c | c | } \hline \text { Women } & \text { Men } \\\hline \bar { x } _ { 1 } = 12.5 \mathrm { hrs } & \bar { x } _ { 2 } = 13.8 \mathrm { hrs } \\\hline s _ { 1 } = 39 . \mathrm { hrs } & s _ { 2 } = 5.2 \mathrm { hrs } \\\hline n _ { 1 } = 14 & n _ { 2 } = 17 \\\hline\end{array}$$ Use a 0.05 significance level to test the claim that the mean amount of time spent watching television by women is
smaller than the mean amount of time spent watching television by men. Include your null and alternative hypotheses,
the test statistic, P-value or critical value(s), conclusion about the null hypothesis, and conclusion about the claim
in your answer.

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Definitions:

Output

The amount of products or services produced by a company, industry, or economy in a specified period.

Labor Demand Curve

A graphical representation showing the relationship between the wage rate and the quantity of labor employers are willing to hire.

Diminishing Returns

A principle stating that if one input in the production of a commodity is increased while other inputs are held fixed, a point will eventually be reached at which additions of the input yield progressively smaller, or diminishing, increases in output.

Imperfectly Competitive

A market structure characterized by many producers that have some control over the prices they charge, but where no single firm dominates the market.