A biologist wishes to estimate the effect of an antibiotic on the growth of a pa

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 = 12 cm2 and that he has a sample size of 35 with sample mean equal to 113 cm2.

(a) What is the standard error of the sample mean? (Use 3 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 .
(   ,   ) (Use 3 decimal places)

Explanation / Answer

a.
Standard Error= sd/ Sqrt(n)
Where,
sd = Standard Deviation
n = Sample Size

Standard deviation( sd )=12
Sample Size(n)=35
Standard Error = ( 12/ Sqrt ( 35) )
= 2.028

b.
t-value: 2.33

c.
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
Mean(x)=113
Standard deviation( sd )=12
Sample Size(n)=35
Confidence Interval = [ 113 ± Z a/2 ( 12/ Sqrt ( 35) ) ]
= [ 113 - 2.33 * (2.028) , 113 + 2.33 * (2.028) ]
= [ 108.274,117.726 ]

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