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Unformatted text preview: Chapter 8 Testing Statistical Hypotheses Section 8.1 1. (a) Yes, > 100 is a statement about a population standard deviation, i.e., a statement about a population parameter. (b) No, this is a statement about the statistic x , not a statement about a population parameter. (c) Yes, this is a statement about the population median ~ . (d) No, this is a statement about the statistic s (s is the sample , not population, standard deviation. (e) Yes, the parameter here is the ratio of two other parameters; i.e, 1 / 2 describes some aspect of the populations being sampled, so it is a parameter, not a statistic. (f) No, saying that the difference between two samples means is 5.0 is a statement about sample results, not about population parameters. (g) Yes, this is a statement about the parameter of an exponential population. (h) Yes, this is a statement about the proportion of successes in a population. (i) Yes, this is a legitimate hypothesis because we can make a hypothesis about the population distribution [see (4) at the beginning of this section]. (j) Yes, this is a legitimate hypothesis. We can make a hypothesis about the population parameters [see (3) at the beginning of this section]. 2. The purpose of inspecting pipe welds in nuclear power plants is to determine if the welds are defective (i.e., do not conform to specifications). So, we assume the welds do conform, H : 100 = , until we have sufficient evidence to claim that the welds are defective, H a : 100 < . 3. Let denote the average amperage in the population of all such fuses. Then the two relevant hypotheses are H : = 40 (the fuses conform to specifications) and H a : 40 (the average amperage either exceeds 40 is less than 40). 4. Let denote the population standard deviation of sheath thickness. The relevant hypotheses are: 05 . : 05 . : < = a H versus H This is because the company is interested in obtaining conclusive evidence that 05 . < . A Type I error would be: concluding that the true standard deviation of sheath thickness is less than .05mm when, in fact, it is not. Chapter 8 Testing Statistical Hypotheses 2 A Type II error would be: concluding that the true standard deviation of sheath thickness is equal to .05mm when, in fact, it is really less than .05mm. 5. Let denote the average breaking distance for the new system. The relevant hypotheses are H : = 120 versus H a : < 120, so implicitly H really says that 120. A Type I error would be: concluding that the new system really does reduce the average breaking distance (i.e., rejecting H ) when, in fact (i.e., when H is true) it doesnt . A Type II error would be: concluding that the new system does not achieve a reduction in average breaking distance (i.e., not rejecting H ) when, in fact (i.e, when H is false) it actually does....
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This note was uploaded on 02/23/2009 for the course STAT 350 taught by Professor Staff during the Fall '08 term at Purdue UniversityWest Lafayette.
 Fall '08
 Staff
 Standard Deviation

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