Question

Six healthy three-year-old female Suffolk sheep were injected with the antibiotic Gentamicin at a dosage of 10mg/kg body weight. Their blood serum concentrations (microgram/mLi) of Gentamicin 1.5 hours after injection were as follows:

32.1 26.3 21.2 32.9 22.9 32.1

For these data, the mean is 27.9 and the standard deviation is 5.2

1. Construct a 95% confidence interval for the population mean.
2. Define in words the population mean that you estimated in part (a).
3. The interval constructed in (a) nearly contains all of the observations; will this typically be true for a 95% confidence interval? Explain.

Answer 1

we have.

u = 27.9, = 5.2, n = 6

a) 95% confidence interval z score = 1.96

Lower limit = u - z*/sqrt(n)

= 27.9 - 1.96*5.2/sqrt(6)

= 23.7

Upper limit = u + z*/sqrt(n)

= 27.9 + 1.96*5.2/sqrt(6)

= 32.1

Thus, confidence interval is (23.7, 32.1)

b) By this 95% confidence interval we can say that there is 95% chance that population mean will lie between 23.7 and 32.1

c) 95% confidence interval gives wide range of observations. However, 99% confidence interval will contain more range of observations (as Z score for 99% confidence level will be more than z score for 95% confidence interval)