A biologist wishes to estimate the effect of an antibiotic on the growth of a pa
ID: 3153332 • Letter: A
Question
A biologist wishes to estimate the effect of an antibiotic on the growth of a particular bacterium by examining the mean amount of bacteria present per plate of culture when a fixed amount of the antibiotic is applied. Suppose he estimates that s = 11 cm2 and that he has a sample size of 35 with sample mean equal to 110 cm2.
(a) What is the standard error of the sample mean? (Use three decimal places)
(b) What is the the t* value needed to construct a 98% confidence interval for the mean?
(c) Let denote the population mean amount of bacteria present per plate of culture. Calculate the 98% confidence interval for .
Explanation / Answer
a)
Note that
SE = s/sqrt(n)
As
s = sample standard deviation = 11
n = sample size = 35
Hence,
SE = 11/sqrt(35) = 1.85933936 [ANSWER]
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b)
As
alpha/2 = (1 - confidence level)/2 = 0.01
df = n - 1 = 34
Thus, by table/technology,
t(alpha/2) = critical t for the confidence interval = 2.441149628 [ANSWER]
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c)
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 = 0.01
X = sample mean = 110
t(alpha/2) = critical t for the confidence interval = 2.441149628
s = sample standard deviation = 11
n = sample size = 35
df = n - 1 = 34
Thus,
Margin of Error E = 4.538925588
Lower bound = 105.4610744
Upper bound = 114.5389256
Thus, the confidence interval is
( 105.4610744 , 114.5389256 ) [ANSWER]
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