4 Biology 4401 Fall 2016 Using Statistics for Estimation: Confidence intervals Due: Monday, 26 September @ 2:00 pm 1. The mean blood cholesterol concentration of a large population of adult males (50-60 years old) is 200 mg/dL with a standard deviation of 20 mg/dL. Assume that blood cholesterol measurements are distributed normally. a. What is the probability that the mean of a sample of 100 men from this age group will have a value greater than 204 mg/dL? How does this compare to the probability that an individual adult male (50-60 years old) will have a value greater than 204 mg/dL? Why are these two probabilities different? b. If a group of 25 older men who are strict vegetarians have a mean blood cholesterol level of 188 mg/dL, would you say that vegetarianism significantly lowers blood cholesterol levels. Explain your answer using statements of probability. 2. A botanist studying understory plants collects 25 plants and finds that the sample of plants have a mean height of 15 cm with a sample variance of 16 cm2. a. Using the data above, calculate the following confidence intervals about the mean, : Lower Limit Upper Limit 80% C.I. 90% C.I. 95% C.I. 99% C.I. b. Using the data above, calculate a 95% C.I. about the variance, 2: Lower Limit Upper Limit 80% C.I. 90% C.I. 95% C.I. 99% C.I. 3. You are employed in a pharmaceutical laboratory testing the efficacy of various experimental drugs on a line of cancer cells. It is important that conditions surrounding tests of candidate drugs be as uniform as possible, including the media used to culture cells, the stage of the logistic growth curve, age and density of cells, etc. Not surprisingly, the protocol for inoculating new cultures, the media, and growth conditions are well established and reliably produce cell cultures with an average density of 120 cells/mm3 within 72 hours of inoculation. A hefty portion of the laboratory budget goes into cell culture, and being a bright young GT Biology graduate, you feel confident that you can do better at growing these cells in an alternate (and much cheaper) medium. The question is, will this new culture medium meet the criteria for density of cells within 72 hours of inoculation? You perform an experiment to test your new \"Buzz media\" by inoculating 25 plates and recording the density of cells at 24-hr intervals: Interval (hrs) n Average cells/mm3 s2 0 25 just inoculated - 24 25 10 144 48 25 25 225 72 25 95 484 96 25 108 625 a. Use these data to calculate 95% confidence intervals around the sample means for each interval. Assume that you can apply the t distribution (i.e. this is a sampling distribution). At what time interval does the 95% confidence interval include 120 cells/mm3? Give a probability statement supporting your argument that Buzz Media is a suitable, cheaper alternative for growing cells. b. Use these data to calculate 95% confidence intervals around sample variance (s2) at 96 hr. If the original method for growing cells had a variance of 320, is the new method sufficiently consistent to provide results as reliable as the old method? Again, use a probability statement to support your conclusion