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:

Ecological Systems Theory

A framework for understanding the complex network of relationships that influence an individual's development, ranging from immediate family settings to broader societal influences.

Microsystem

A term in ecological systems theory referring to the immediate environments with which an individual interacts, such as family and school.

Mesosystem

The interlocking settings that influence the child, such as the interaction of the school and the larger community.

Incorporates

To include or integrate parts into a whole, often referring to the inclusion of multiple aspects or elements into a single entity.