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Chapter5 Examples

# Chapter5 Examples - Chapter 5 Estimation and Confidence...

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Chapter 5: Estimation and Confidence Intervals (will be modified until end of chapter5) Section 5.1 and 5.2 are reading exercises Section 5.3: Population mean 1. Large companies spend on average \$2500/year in covering health insurance of a blue-collar worker (family of four). A company’s, Valmart, health coverage of its blue-collar workers is questioned. How do we prove whether Valmart is a good provider of health benefits to blue-collar workers? 2. Millions of ball bearings (with required mean diameter=.5) are imported from a foreign country. A quality control inspector put to the task to accept/reject the shipment. What should this inspector do? 3. The mean score (w/o any training class) of a large insurance company annual agent qualification test is 70. The owner proposes one week new training classes before the test. How do we prove whether the new training classes are effective in improving the mean test scores? The above questions can be answered several ways using the following statistical theory. valmart ball bearings After Training HealthCareCost Diameter Test Scores 1850 0.48 75 1361 0.5 75 2122 0.49 77 2638 0.52 67 2599 0.53 79 2867 0.48 80 908 0.49 74 1883 0.47 84 2548 0.46 92 1457 0.51 76 1655 76 1155 78 1077 80 1511 87 1613 72 941 78

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1716 72 1798 78 2067 77 1817 76 1837 70 1815 71 2671 77 1957 77 1907 76 1743 2986 2433 3188 1673 Theory X is a RV (population) with unknown population mean (true mean) μ and with unknown population standard deviation (true stdev) σ . First collect a simple random sample of size n. SRS: n x x x , , , 2 1 STATISTICAL tools: a. calculate point estimate of b. calculate C confidence interval for a. sample mean x is the point estimate and similarly s is the point estimate of . Definition: Provided that the following assumptions are true: 1. we have a SRS, 2. we have a normal population then t = ) ( n s x - has t-distribution with parameter degrees of freedom (df) = n-1. Notes: 1. ) ( n s is known as the standard error (se) of the sample mean. 2. As n gets closer to , the t-distribution becomes z-distribution. t-table gives the top or upper a percentile at df=n-1 and it is represented 1 , - n a t . Locate a in the top row, cross out the corresponding column, and df in the left-most column, cross
out the corresponding row. The intersection gives the number for 1 , - n a t . The lower a percentile at df=n-1 is represented as

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Chapter5 Examples - Chapter 5 Estimation and Confidence...

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