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[See Steps] In order to attribute changes in nest activity to the active influence of the queen, 9 nests were randomly selected for experimental treatment.

Question: 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

Queens and Workers: Experimental Treatments

Normal treatment: The observations were made of the undisturbed state of the nest as originally located.
The queen was removed from the nest for about an hour.
The queen was removed to a cool environment, making her inactive, and returned to the nest; thus, she is present in the nest, but not able to interact with the worker wasps.
Queen removed: Queen cooled/inactive:

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.)

Workers Activity Levels

Colony # Normal
(Undisturbed) 		Queen
Removed 		Queen Cooled/
Inactive
1 0.18 0.06 0.03
2 0.16 0.19 0.18
3 0.06 0.17 0.05
4 0.46 0.33 0.24
5 0.11 0.17 0.14
6 0.37 0.23 0.11
7 0.32 0.25 0.06
8 0.59 0.40 0.29
9 0.43 0.31 0.37

Partial summary of data

Treatment Lower Quartile Median Upper Quartile
Normal 0.135 0.32 0.445
Q. Removed 0.17 0.23 0.32
Q Cooled/Inactive 0.055 0.14 0.265

4

  1. 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? (4 points)
  2. 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:
    1. "Approximately 95 % of the undisturbed activity levels will be within 2 standard deviation of the mean."
      OR
      II. II. "At least 75 % of the undisturbed activity levels will be within 2 standard deviation of the mean."
      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 (hint: you may want to check the distribution of the data by using stemand-leaf diagram or histogram. It’s your choice.) (6 points)
  3. Using your recommended procedure from part (e) what percentage should be used to fill in the blank in the appropriate statement? (5 points)

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