Construct a Confidence Interval For $\mu _ { \mathrm { d } }$

question 108

Essay

Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-A researcher obtained independent random samples of men from two different towns. She recorded the weights
of the men. The results are summarized below: $$\begin{array} { l l } \frac { \text { Town A } } { \mathrm { n } _ { 1 } = 41 } & \frac { \text { Town B } } { \mathrm { n } _ { 2 } = 21 } \\\overline { \mathrm { x } _ { 1 } } = 165.1 \mathrm { lb } & \overline { \mathrm { x } } _ { 2 } = 159.5 \mathrm { lb } \\\mathrm { s } _ { 1 } = 25.2 \mathrm { lb } & \mathrm { s } _ { 2 } = 25.1 \mathrm { lb }\end{array}$$ Use a 0.05 significance level to test the claim that there is more variation in weights of men from town A than in
weights of men from town B.

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Definitions:

Explanatory Variable

A type of variable in statistical modeling that is used to explain variations in the dependent variable; it is also known as an independent variable.

Quantitative Variables

Variables that represent numerical amounts or quantities, which can be measured and expressed numerically.

Associated

Pertains to the connection or relationship between two or more variables or factors.

Response Variable

The outcome or variable of interest that is measured or observed in a study, experiment, or analysis to see how it is affected by explanatory variables.