Question

In: Statistics and Probability

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

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.

Expert Solution

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 = t_{0.005,34 = 2.73}

t_/2,df = 2.73

Margin of error = E = t_/2,df * (s / $\sqrt$ n)

= 2.73 * (14 / $\sqrt$ 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)

orchestra answered 2 years ago

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