The Weights of Five Players on a Football Team Are

question 55

Essay

The weights of five players on a football team are shown below. $$\begin{array} { r | c c c c c } \text { Player } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\ \hline \text { Weight (lb) } & 290 & 310 & 250 & 255 & 220 \end{array}$$ Consider these players to be a population of interest. The mean weight, µ, for the population is 265 pounds. Construct a table that shows all of the possible samples of size two. For each of the possible samples, list the players in the sample, their weights, and the sample mean. The first line of the table is shown below. $$\begin{array} { c | c | c } \text { Sample } & \text { Weights } & \overline { \mathrm { x } } \\ \hline \mathrm { A } , \mathrm { B } & 290,310 & 300 \end{array}$$ Use your table to find the probability that, for a random sample of size two, the sample mean will equal the population mean.

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Definitions:

Significance Level

The probability of rejecting the null hypothesis when it is true, often denoted by alpha.

Population Variances

A measure of the dispersion or spread of a set of data points in a population in terms of its mean, indicating how far the values lie from the average.

Clinic Waiting Time

The duration a patient spends waiting to be seen by a healthcare professional after their appointment time or upon arrival.

Interval Estimate

A variety of values, gathered from sample sources, that is considered likely to envelop the value of a mysterious population parameter.