Test the Claim That the Samples Come from Populations with the Same

question 8

Essay

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance.
-Given the sample data below, test the claim that the populations have the same mean. Use a significance level of 0.05.
$\begin{array} { l } \text { Brand A }&\text { Brand B }&\text { Brand C }&\text { Brand D }\\\hline\mathrm{n}=16 & \mathrm{n}=16 & \mathrm{n}=16 & \mathrm{n}=16 \\\overline{\mathrm{x}}=2.09 & \overline{\mathrm{x}}=3.48 & \overline{\mathrm{x}}=1.86 & \overline{\mathrm{x}}=2.84 \\\mathrm{~s}=0.37 & \mathrm{~s}=0.61 & \mathrm{~s}=0.45 & \mathrm{~s}=0.53\end{array}$

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Definitions:

Native American Land

Land historically occupied or used by Indigenous peoples of the Americas, often subject to disputes and treaties over sovereignty and rights.

Seventeenth Century

refers to the period from 1601 to 1700 in the Gregorian calendar, marked by significant cultural, political, and scientific developments.

Jamestown Colony

The first permanent English settlement in North America, established in 1607 in present-day Virginia.

John Smith

An English soldier, explorer, colonial governor, and one of the founding leaders of the Jamestown colony in Virginia in the early 17th century.