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.

---

Definitions:

Pain Threshold

The minimum intensity of a stimulus that is perceived as painful, varying significantly among individuals and influenced by biological, psychological, and environmental factors.

Referred Pain

A phenomenon where pain felt in a part of the body is actually caused by injury or illness elsewhere in the body.

Central Sensitization

A condition of the nervous system that is associated with the development and maintenance of chronic pain.

Peripheral Sensitization

An increase in the sensitivity of sensory neurons in the peripheral nervous system, typically leading to an exaggerated response to pain or touch.