Confidence interval and hypothesis test
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Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation (sigma). Assume that the population has a normal distribution.
8) A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the standard deviation of the scores of all subjects.
Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly
selected from a population with a normal distribution.
9) In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures.
Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures.
518 548 561 523 536
499 538 557 528 563
At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours.
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Solution Summary
This solution gives a detailed, step-by-step example showing how to find a confidence interval for the population standard deviation. It also has an example of a small sample hypothesis test (a t-test) for a population mean.
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