Researchers examined the mechanical properties of webs spun

Researchers examined the mechanical properties of webs spun by the orb spider, Nephelia edulis. A table in the publication reports summary statistics for a number of variables in the form of the mean plus or minus the standard error of the mean. This form is very common in scientific publications. For 15 adult female spiders, web areas (in centimeter2) are 634±30. What are and s for these 15 spider webs? 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

Solution

Given the data mean plus or minus the standard error of the mean = 634±30
standard error of the mean = 30
Standard Error= sd/ Sqrt(n)
Where,
sd = Standard Deviation
n = Sample Size

Standard deviation( sd )=Unknown
Sample Size(n)=30
Standard Error = ( 400/ Sqrt ( 15) )
30 = ( sd/ Sqrt ( 15) )
sd = 30 * Sqrt ( 15) = 116.1895

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Confidence Interval = [ 634 ± Z a/2 ( 116.1895/ Sqrt ( 30) ) ]
= [ 634 - 1.96 * (21.213) , 634 + 1.96 * (21.213) ]
= [ 592.422,675.578 ]