Chapter 11

Chapter 11 - Chapter 11 Hypothesis Testing Continued 1...

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1 Chapter 11: Hypothesis Testing Continued 1. Steps for Hypothesis Testing a. State the null hypothesis and the alternate hypothesis b. Specify an acceptable risk of rejecting the null hypothesis when it is true c. Select the test statistic and list the assumptions of the test statistic d. Formulate the decision rule and draw a graph e. Obtain a random sample of size n from the population, compute the test statistic, and make a decision about the null hypothesis and alternative hypothesis. State decision. 2. List of Tests a. One Sample Tests: i. Z Test ii. T Test iii. Proportions Test iv. Correlation Test b. Two Sample Tests: i. Independent Samples: 1. Z Test 2. Pooled T Test 3. Separate Variance T Test 4. Proportions Test ii. Dependent Samples: 1. Paired T Test 3. One Sample Tests in Depth a. One Sample Z Test i. Hypothesis 1. :,, o ooo H μ μμ μμ μ = ≥≤ 2. Ao o o H <> ii. Test Statistic o x z n σ =
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2 iii. Assumptions 1. Random sampling 2. Normality or large sample 3. Variance or standard deviation of population is known iv. Confidence Interval 1. Two Sided Confidence Interval 22 Xz nn αα σ μ −< < + 2. Confidence Interval for 0 : A H > n α >− 3. Confidence Interval for 0 : A H < n <+ v. Example: The Minnesota Multiphasic Personality Inventory test measures the level of psychopathic deviance, a measure of anti- social tendencies. The test was given to a random sample of 30 men classified as habitual criminals. The researchers want to know if habitual criminals have greater anti-social tendencies then non- criminals. The population of non-criminals is known to be normally distributed, with mean and standard deviation equal to 50 and 10. Participant Pd Scale Participant Pd Scale 1 50 16 55 2 51 17 56 3 54 18 48 4 55 19 45 5 25 20 41 6 61 21 82 7 64 22 65 8 55 23 67 9 55 24 75 10 52 25 40 11 71 26 61 12 57 27 35 13 59 28 56 14 54 29 56 15 55 30 55
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3 (MEGASTAT) Hypothesis Test: Mean vs. Hypothesized Value 50.000 hypothesized value 55.167 mean Pd Scale 11.335 std. dev. 2.070 std. error 30 n 2.50 z .0063 p-value (one-tailed, upper) b. One Sample T Test i. Hypothesis 1. :,, o ooo H μ μμ μμ μ = ≥≤ 2. Ao o o H <> ii. Test Statistic / o x t sn = , df = n-1 iii. Assumptions 1. Random sampling 2. Normality 3. Variance or standard deviation of population is NOT known iv. Confidence Interval 1. Two Sided Confidence Interval 22 ss Xt nn αα −< < +
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4 2. Confidence Interval for 0 : A H μ > s Xt n α >− 3. Confidence Interval for 0 : A H < s n <+ v. Example: Students desiring to enter graduate school at Baylor are required to submit Graduate Record Examination (GRE) scores with their applications. The verbal scores for a random sample of 20 applications received this year are the following: Participant GRE Score Participant GRE Score 1 402 11 429 2 381 12 410 3 430 13 406 4 376 14 382 5 395 15 410 6 390 16 391 7 407 17 403 8 413 18 398 9 424 19 410 10 360 20 404 Baylor University believes that this years students applying for graduate school are not as good at grammar and reading than previous years. Last years verbal scores averaged 400.
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This note was uploaded on 04/30/2008 for the course QBA 2302 taught by Professor Dr.lohaka during the Spring '08 term at Baylor.

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Chapter 11 - Chapter 11 Hypothesis Testing Continued 1...

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