Statistics for laboratory scientists

Homework problems for lecture 13

1. [Problem 7.3, Sokal & Rohlf, pg 177] The 95% confidence limits for mu as obtained in a given sample were 4.91 and 5.67g. Is it correct to say that 95 times out of 100 the population mean, mu, falls inside the interval from 4.91 to 5.67g? If not, what would the correct statement be?

2. We are interested in estimating the concentration of substance X in the Baltimore water supply on the basis of measurements of a number of samples. Suppose measurements of such samples will be approximately normally distributed with unknown mean (the true concentration) and known SD = 1.5 ppb.

   How many samples should we measure if we wish our 95% confidence interval for the true concentration to have width < 1 ppb?

3. We obtain the log₁₀ gene expression for 5 tissue samples, as follows:

   3.52

   3.89

   3.13

   3.66

   3.28

   Suppose that such measurements are independent and are normally distributed with mean mu and SD sigma.

   Provide a 95% confidence interval for mu.