AMS 572 Practice for Midterm, #2
Fall 2006A
1. In a standard dissolution test for tablets of a particular drug product, the manufacturer must obtain the dissolution rate of for a batch of tablets prior to release of the batch. Suppose that the dissolution test consists of assays for 32 randomly selected individual 25 mg tablets. For each test, the tablet is suspended in an acid bath and then assayed after 30 minutes. The results of the 32 assays are given here:
18.519.719.720.419.220.819.620.2
19.919.218.619.820.519.119.719.9
18.019.720.620.419.920.018.218.0
19.117.919.920.018.418.319.319.4
(a) Please make a point estimate of the mean dissolution rate for the batch of tablets.
(b) Please use this information to calculate a 95% confidence interval of the mean dissolution rate for the batch of tablets.
(c) (1) At significant level 0.05, can you conclude that the batch of pills has a mean dissolution rate less than 19.5 mg?
(2) What is the p-value of your test?
(d) If the actual mean dissolution rate for the batch of tablets is 19.2, please calculate the power of your test.
(e) If we want to improve the power to 85%, what sample size should we have?
2. To study the effectiveness of wall insulation in saving energy for home heating, the energy consumption (in MWh) for 5 houses in Bristol, England, was recorded for two winters; the first winter was before insulation and the second winter was after insulation.
House 1 2 3 4 5
Before 12.1 10.6 13.4 13.8 15.5
After 12.0 11.0 14.1 11.2 15.3
(a) Please provide a 95% confidence interval for the difference between the mean energy consumption before and after the wall insulation is installed. What assumptions are necessary for your inference?
(b) Can you conclude that there is a difference in mean energy consumption before and after the wall insulation is installed at the significance level 0.05?Please test it and evaluate the p-value of your test. What assumptions are necessary for your inference?
(c) Please write a SAS program to perform the test and examine the necessary assumptions given in (b).
3a. 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. Previous experimentation with the antibiotic on this type bacterium indicates that the standard deviation of the amount of bacteria present is approximately12. It is also reasonable to assume a normal distribution. Use this information to determine the number of observations to estimate the mean amount of bacteria present with a maximum error of 6. Please first derive the general formula for sample size calculation based on a maximum error of E.
3b. Show that Y1 and Y2 are independent i.f.f..