For 15 adult female spiders web areas in centimeter2 are 634

For 15 adult female spiders, web areas (in centimeter²) are 634 30.

1) What are and s for these 15 spider webs?

2) 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

Hi! Some symbols did not register well, but I assumed you meant that the sample mean was X = 634, with standard deviation of 30.

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1)

It has the same same mean, u(X) = 634 cm^2. [ANSWER]

It has a standard deviation of

s(X)= s/sqrt(n) = 30/sqrt(15) = 7.745966692 [ANSWER]

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2.

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    634          
t(alpha/2) = critical t for the confidence interval =    2.144786688          
s = sample standard deviation =    30          
n = sample size =    15          
df = n - 1 =    14          
Thus,              
Margin of Error E =    16.61344625          
Lower bound =    617.3865538          
Upper bound =    650.6134462          
              
Thus, the confidence interval is              
              
(   617.3865538   ,   650.6134462   ) [ANSWER]