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# MAT221-2006Fall - M AT 2 21 F inal B December 1 3 2 006 N...

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MAT 221 Final B (December 13, 2006) Name: _ Instructor's name: _ 1. There are 8 problems and a total of 9 pages in this booklet. 2. Show all of your work and label your answers clearly. 3. If you use a table, state the table used: for example 1.887 (from Table A). 4. If you use a function on the TI 83 (or TI 89), write out the command you entered as well as the result: for example, 0.0668 (normalcdf (-10, -1.5, 0.1)). 1 2 3 4 5 6 7 8 I Total] __ 1

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1. (12 pts) Suppose that a student measuring the boiling temperature of a certain liquid observes the six readings and obtained the sample mean of 101.8 (in degrees Celsius). Also assume that the standard deviation for this procedure ((j) is 1.2 degrees. (a) Construct a 95% confidence interval for the mean boiling temperature of this liquid. (b) Suppose that you were dissatisfied with the width of the confidence interval, and wanted to cut the margin of error to ±O.5, keeping the same confidence level of 95%. How many readings (total) would have to be included in the new sample? 2
2. (13 pts) The level of calcium in the blood of healthy young adults follows a normal distribution with mean JL = 10 milligrams per deciliter and standard deviation (J = 0.5. A clinic measures the blood calcium of 27 healthy pregnant young women at their first visit for prenatal care. The mean of these 27 measurements is x = 9.8. Is this evidence that the mean calcium level in the population of healthy pregnant young women is less than 1O? (a) Set up the null and alternative hypotheses that you will be testing regarding the above question. (b) Assuming that the distribution of calcium level measurements for pregnant young women is a normal distribution with (J = 0.5, find the value of the test statistic and compute the P-value.

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