In: Statistics and Probability
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 = 14 cm2 and that he has a sample size of 35 with sample mean equal to 115 cm2. Assume all conditions are met.
(a) What is the the t* value needed to construct a 99% confidence interval for the mean?
*NOTE 2.783 IS WRONG and so is 2.441
(b) Let μ denote the population mean amount of bacteria present per plate of culture. Calculate the 99% confidence interval for μ.
Solution :
Given that,
Point estimate = sample mean =
= 115
sample standard deviation = s = 14
sample size = n = 35
Degrees of freedom = df = n - 1 = 35-1 = 34
a) At 99% confidence level
= 1-0.99% =1-0.99 =0.01
/2
=0.01/ 2= 0.005
t/2,df
= t0.005,34 = 2.73
t
/2,df = 2.73
Margin of error = E = t/2,df
* (s /
n)
= 2.73 * (14 /
35)
Margin of error = E =6.46
b) The 99% confidence interval estimate of the population mean is,
- E <
<
+ E
115 - 6.46<
< 115+6.46
108.54 <
< 121.46
(108.54,121.46)