In Order to Attribute Changes in Nest Activity to the Active

question 23

Essay

In order to attribute changes in nest activity to the active influence of the queen, 9 nests were randomly selected for experimental treatment. The normal activity of the nests were measured, and treatments were administered as described below: The data for the control treatment and each of the experimental treatments is given in the table below. The Activity Levels are the average proportion of active nest time for workers who were present in the normal and two experimental treatment periods. For example, 0.50 would mean for that nest the average amount of time the workers were actively working was 0.50 of the available time during that treatment. (The colony numbers are for identification in the table only.) ​ ​
(a) Construct comparative box plots of the active nest times for (a) normal, (b) Queen removed, and (c) Queen Cooled/Inactive. (Note: since the data are proportions, there are no actual units for the data.)
(b) Two current theories about the queen's interaction with workers are that (A) the queen increases worker activity by her mere presence, or (B) she increases worker activity by interacting with worker bees. Based on your plot in part (a), which theory--if either--is supported by the data? Justify your conclusion with an appropriate statistical argument.
(c) What are the mean and standard deviation of the proportion of worker activity for undisturbed wasp nests. = s =
(d) One of the nests (Colony #4) has a proportion of worker activity of 0.46. How many standard deviations above/below the mean is the worker activity level in this nest?
(e) The biologists would like to provide some explanatory information for other scientists who would be using their new scale. They would like to state something like the following:
I. "Approximately _____ % of the undisturbed activity levels will be between −2σ and 2σ." OR
II. "At least _____ % of the undisturbed activity levels will be between −2σ and 2σ."
Based on your work so far, would you recommend using the Empirical Rule or Chebyshev's Rule to establish this percentage? Explain your reasoning in a few sentences.
(f) Using your recommended procedure from part (e) what percentage should be used to fill in the blank in the appropriate statement?

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Definitions:

Cartel Agreement

An arrangement among competing firms to control prices or exclude entry of a new competitor in the market, often through setting production levels or dividing markets.

Nash Equilibrium

A concept in game theory where no player can benefit by unilaterally changing their strategy if the strategies of the others remain unchanged.

Dominant Strategy

A strategy in game theory that provides the best outcome for a player, regardless of the strategies chosen by other players.

Monopoly Outcome

The result or situation where a single company or entity has exclusive control over a particular commodity or service, often leading to higher prices and lower quality.