ESTIMATION
EXERCISES
For each of the following exercises construct 90, 95, and 99 percent confidence intervals for the population mean, and state the practical and probabilistic interpretation of each. Indicate which interpretation you think would be more appropriate to use when discussing confidence intervals with someone who has not had a course in statistics, and state the reason for your choice. Explain why the three intervals that you construct are not of equal width. Indicate which of the three intervals you would prefer to use as an estimate of the population mean, and state the reason for your choice.
6.2.1: We wish to estimate the average number of heartbeats per minute for a certain population. The average number of heartbeats per minute for a sample of 49 subjects was found to be 90. Assume that these 49 patients constitute a random sample, and that the population is normally distributed with a standard deviation of 10.
ANSWER
(a) 88.92
(b) 87.93
(c) 86.94
6.2.5. some studies of Alzheimer s disease (AD) have shown an increase in CO2 production in patients with the disease. In one such study the following bCO2 values were obtained from 16 neocortical biopsy samples from AD patients
1009
1280
1180
1255
1547
2352
1956
1080
1776
1767
1680
2050
1452
2857
3100
1621
Assume that the population of such values is normally distributed with standard deviation of 350.
ANSWER
1576.125, 1919.125
THE t DISTRIBUTION
EXERCISES
6.3.1: Use the t distribution to find the reliability factor for a confidence interval based on the following confidence coefficients and sample sizes:
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a b c d
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Confidence coefficient 0.95 0.99 0.90 0.95
Sample size 15 24 8 30
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ANSWER
(a) 2.1448
(b) 2.8073
(c) 1.8946
(d) 2.0452