Use the Data Given Below to Verify That the T $$\begin{array} { c | c } \mathrm { A } & \mathrm { B } \\\hline 85 & 74 \\81 & 72 \\73 & 65 \\91 & 83 \\64 & 59\end{array}$$

question 35

Essay

Use the data given below to verify that the t test for independent samples and the ANOVA method are equivalent. $$\begin{array} { c | c } \mathrm { A } & \mathrm { B } \\\hline 85 & 74 \\81 & 72 \\73 & 65 \\91 & 83 \\64 & 59\end{array}$$ i)Use a t test with a 0.05 significance level to test the claim that the two samples come from populations with the same means. ii)Use the ANOVA method with a 0.05 significance level to test the same claim. iii)Verify that the squares of the t test statistic and the critical value are equal to the F test statistic and critical value.

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Definitions:

Demographic Transition

Refers to the transition from high birth and death rates to lower birth and death rates as a country or region develops from a pre-industrial to an industrialized economic system.

Population Growth

The increase in the number of individuals in a population, measured by the natural increase and net migration.

Per Capita Incomes

The average income earned per person in a certain area or country, calculated by dividing the area's total income by its population.

Birth Rates

The average number of births per 1,000 people in a given population during a specific period of time.