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MM207 Unit 6: Confidence Intervals for Means and Population Proportions

Discusses confidence intervals and their application in statistics.

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    MM207 Unit 6 Chapter 6 Project ROBYN GALINDO 1 MM207 Unit 6: Confidence Intervals for Means and Population Proportions Total points are 4 0 . Points are included with each problem. Included with each section or problem are reference examples and end of section exercises that can be used as a guide. Be sure to show your work in case partial credit is awarded . To receive full credit, work must be shown if applicable. Section 6.1: Confidence Intervals for the Mean (Large Samples) 1. Find the critical value z c necessary to form a confidence interval at the given level of confidence. (Re ferences: definition for level of confidence page 311 , end of section exercises 5 – 8 page 317) ( 2 .5 points each) a. 90 % ½ (1 - .90) = 0 .05 = 1.645 b. 80 % ½ (1 - .80) = 0.10 = 1.28 2. The new Twinkle bulb has a standard deviation 35   hours. A random sample of 50 light bulbs is selected from inventory. The sample mea n was found to be  X 55 0 hours. a. Find the margin of error E for a 90% confidence interval . (5 points) Round your answer to the nearest hundredths. . (References: definition of margin of error on page 312 and example 2 on page 312). E = 1.645 (35/ √ 50) = 8.14 b. C ons truct a 90 % confidence interval for the mean life,  of all Twinkle bulbs. (5 p oints) ( References: example 5 page 315 , end of section exercises 51 - 56 pages 319 - 320) Left Endpoint: 550 – 8. 14 = 541.86 Right Endpoint: 550 + 8.14 = 558.14 541.86 < μ < 558.14 3 . A standard placement test has a mea n of 115 and a standard devi ation of  = 10 . Determine the minimum sample size if we want to be 90% certain that we are within 2 points of the true mean. ( References: example 6 page 316 , end of section exercises 58 - 62 pages 321 - 322) ( 5 points) n = (1.645)(10) ² = 271 Section 6.2: Confidence Intervals for the Mean (Small Samples)

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