test3 - 2. A manufacturer of gunpowder has developed a new...

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STA2023 Class Test 3, Tuesday 23 November 1. Acid rain, caused by the reaction of certain air pollutants with rainwater, appears to be a growing problem in the northeastern section of the United States. Pure rainfall through clean air registers a pH reading of 5.7. Suppose that water samples from 40 rainfalls are taken randomly from the section and analyzed for pH reading. The mean and standard deviation of the 40 readings are calculated to be 3.7 and 0.5 respectively. (a) Suppose the purpose of the study is hopefully to show that the mean pH reading of rainwater in this section is not equal to 5.7. Formulate suitable null and alternative hypotheses. (b) Carry out a test at α =5% of your hypotheses in (a). State clearly the conclusions you draw. (c) State clearly the assumptions required for the test in (b). (d) Explain the meaning of =5% in the test. (e) Calculate the p-value of the observed test statistics. (Assume that P Z { . } . = 26 64 0 0000 , where Z denotes a standard normal random variable)
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Unformatted text preview: 2. A manufacturer of gunpowder has developed a new powder that is designed to produce a muzzle velocity of 3000 feet per second. In order to assess the true mean muzzle velocity, eight shells were loaded with the charge and the muzzle velocities were measured. The mean and standard deviation of the sample are calculated to be 2958.75 and 39.26 respectively. (a) Calculate a 95% confidence interval for the mean muzzle velocity. (b) State clearly the assumptions required for using the confidence interval in (a) (c) How would you interpret the confidence interval in (a) ? 3. In order to assess the proportion, p, of all US households that have a computer, a sample of 6841 US households are selected at random, of which 2470 have a computer. (a) Construct a 95% confidence interval for p. (b) If a 95% confidence interval for p of width 0.01 is required, how large should the sample size be? Give your reasoning....
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This note was uploaded on 08/30/2011 for the course STA 2023 taught by Professor Bagwhandee during the Fall '07 term at University of Central Florida.

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test3 - 2. A manufacturer of gunpowder has developed a new...

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