Ch_16.pdf

# 1728 chapter 16 tests of significance example 1 an

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Chapter 16 Tests of Significance Example 1: An insurance company is reviewing its current policy rates. When originally setting their rates they believed that the average claim amount was \$1,800. They are concerned that the true mean is actually higher than this because they could potentially lose a lot of money. They randomly select 40 claims and calculate the average as \$1,950. Assume that the claim amounts follow a normal distributin with standard deviation \$500. Use = 0 . 05 to test to see if the insurance company should be concerned. 18/28
Chapter 16 Tests of Significance Example 2: A paint manufacturer advertises that one gallon of its paint will cover 400 square feet of an interior wall. Some local painters suspect the average coverage is considerably less and decide to conduct an experiment to find out. What is the null and alternative hypotheses to be tested? What would be the test statistic if a random sample of 5 cans of paint are taken and an average coverage of 380 square feet? Assume all conditions are met and the standard deviation is 20 square feet. What is the conclusion of the test? 19/28

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Chapter 16 Tests of Significance MC Example 1: Suppose we are testing the null hypothesis H 0 : μ = 14 and the alternative H a : μ 6 = 14 for a normal population with σ = 0 . 15 . A random sample of six observations is drawn from the population and we find the sample mean of these observations is 14.133. The P-value is (A) 0.015 (B) 0.030 (C) 0.1867 (D) 0.3734 (E) None of the above 20/28
Chapter 16 Tests of Significance MC Example 2: A supplier advertises that their new energy e ffi cient compact fluorescent light bulbs last for a full year of illumination. A major purchaser of these bulbs takes a random sample of some bulbs and measures their actual lifetimes. If μ is the mean lifetime of the bulbs in years, the hypotheses we would test in order to prove that the supplier is exaggerating (i.e. the mean lifetime is really less than one year) are: (A) H 0 : μ < 1 versus H a : μ = 1 (B) H 0 : μ = 1 versus H a : μ > 1 (C) H 0 : μ > 1 versus H a : μ = 1 (D) H 0 : μ = 1 versus H a : μ < 1 (E) None of the above 21/28

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Chapter 16 Tests of Significance MC Example 3: Levels of blood sugar (glucose) in diabetics will have levels above 1.2 g/L. Laboratory tests for measuring blood glucose have a standard deviation of around 0.01 g/L. Given a single measurement, we would like to test the null hypothesis that a person is not diabetic, against the alternative that she is. Assuming that the measured level from a laboratory test has a normal distribution, if the measurement is 1.21 g/L, the p -value for the test is: (A) 0.16 (B) 0.84 (C) 0 (D) 0.54 22/28
Chapter 16 Tests of Significance Using Confidence Intervals to Perform Hypothesis Tests I We can use the two–sided confidence intervals to perform a two–sided significance test.

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