Use the Two-Proportions Z-Test to Perform the Required Hypothesis Test

question 30

Essay

Use the two-proportions z-test to perform the required hypothesis test. Assume that independent simple randomsamples have been selected from the two populations. Use the critical-value approach.
-In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450 people aged 25-29, 14% were smokers. Do the data provide sufficient evidence to conclude that the proportion of smokers in the 20-24 age group is different from the proportion of smokers in the 25-29 age group? Use a significance level of 0.01.

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Definitions:

Contribution Margin Ratio

A measure indicating the percentage of each sales dollar that contributes to covering fixed costs and generating profit, calculated as (Sales Revenue - Variable Costs) / Sales Revenue.

Fixed Costs

Costs that do not vary with the level of production or sales, such as rent, salaries, and insurance premiums, providing predictability in budgeting.

Break Even

It is the point at which total costs and total revenues are equal, meaning there is no profit or loss.

Operating Income

Earnings before interest and taxes (EBIT), representing a company’s profit from its core business operations.