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 = 15
cm^{2} and that he has a sample size of 35 with sample mean
equal to 111 cm^{2}. Assume all conditions are
met.

(a) What is the the t* value needed to construct a 99%
confidence interval for the mean?

(b) Let μ denote the population mean amount of bacteria present per
plate of culture. Calculate the 99% confidence interval for μ.

Answer #1

a)

df = n -1 = 35 - 1 = 34

t critical value at 0.01 level at 34 df =
**2.728**

b)

99% confidence interval for is

- t * S / sqrt( n) < < + t * S / sqrt( n)

111 - 2.728 * 15 / sqrt(35) < < 111 + 2.728 * 15 / sqrt(35)

104.08 < < 117.92

99% CI is **( 104.08 , 117.92 )**

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