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```CI_Means – The Monarch Butterfly Wing Area Example
Use the information in the following setting to answer questions 1 through 9
As part of a larger study designed to characterize the body features of monarch
butterflies that are found in California researchers captured many specimens from
Oceano Dunes State Park. One of the variables of interest was the wing area. The data
in Table 1 below are the results from 14 male specimens. Output 1 reports the
descriptive statistics for the wing area data. The investigators would like to estimate the
averge wing area of all male monarchs in California during the season that the study
was completed.
[Source: Samuels,M.L.,Witmer,J.A.,Schaffner,A.A, Statistics for
the Life Sciences, 2012, pp 170-1, Pearson Ed, Boston]
Table 1: Monarch Butterfly Wing Areas (cm2)
33.9
32.0
33.0
28.0
30.6
32.0
36.6
32.2
36.5
32.2
34.0
32.3
36.1
30.0
Output 1: Descriptive statistics for the monarch butterfly wing area data
Variable
wing
N
14
Mean
32.814
SE Mean
0.662
StDev
2.476
Minimum
28.000
Q1
31.650
Median
32.250
Q3
34.525
Maximum
36.600
1) This study can be classified as a(n):
A) Observational Study
B) Controlled Experiment
2) Assume that this is a representative sample from the population of all male monarch
butterflies in California during the season; the point estimate for the true average
wing area for this population on this instrument is:
3) Again assume that this is a representative sample from the population of all male
monarch butterflies in California during the season; the point estimate for the true
standard deviation is:
4) The investigators wish to construct a 90% confidence interval (CI) for the true average
wing area in the target population. Based on this, the table value used to compute
the bound (margin of error) on the estimate is:
Gumina/Hunter
CI_Means-Monarch Wing Area.docx
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CI_Means – The Monarch Butterfly Wing Area Example
5) The 90% bound (B) on the estimated wing area is:
6) Construct the 90% CI for the true average wing area for the target population
7) The English interpretation of the interval computed in Problem 6 is:
8) Based on the result from Problem 7 construct the corresponding CI diagram:
9) A recent report claimed that the average wing area for male monarch butterflies in
California during the season is 35 cm2. Based on the results from Problems 7 and 8
would you agree or disagree with this claim?
Agree
Disagree
10) Defend your choice for Problem 9. If you answered ‘agree’ then state the direction
of the difference and discuss the rationale for your conclusion.
Gumina/Hunter
CI_Means-Monarch Wing Area.docx
Page 2 of 3
CI_Means – The Monarch Butterfly Wing Area Example
Output 2: CI and hypothesis test results for the wing area study
One-Sample T: wing
Test of mu = 35 vs not = 35
Variable
wing
N
14
Gumina/Hunter
Mean
32.814
StDev
2.476
SE Mean
0.662
95% CI
(31.385, 34.244)
T
-3.30
P
0.006
CI_Means-Monarch Wing Area.docx
Page 3 of 3
```
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