Researchers examined the mechanical properties of webs spun by the orb spider, N
ID: 3254566 • Letter: R
Question
Researchers examined the mechanical properties of webs spun by the orb spider, Nephelia edulis. A table in the publication gave the summary data (mean 633, standard error 34 cm2
) for the web area of 15 female orb spiders. Assuming an approximately Normal distribution of web areas, and assuming that we can regard these 15 female orb spiders as an SRS of the population of all female orb spiders, give the 95% confidence interval for the web area
in this population.
The 95% confidence interval (±
0.01) is from to cm2
NOTE: The numerical values in this problem have been modified for testing purposes.Researchers examined the mechanical properties of webs spun by the orb spider, Nephelia edulis. A table in the publication gave the summary data (mean 633, standard error 34 cm2
Explanation / Answer
Solution:-
The formula for estimation is:
= M ± Z(sM)
where:
M = sample mean
Z = Z statistic determined by confidence level
sM = standard error = (s2/n)
Calculation
M = 633
t = 1.96
sM = (342/15) = 8.78
= M ± Z(sM)
= 633 ± 1.96*8.78
= 633 ± 17.21
You can be 95% confident that the population mean () falls between 615.79 and 650.21.
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