Probability and Confidence Intervals in Statistics: Quiz Questions, Quizzes of Probability and Statistics

Download Probability and Confidence Intervals in Statistics: Quiz Questions and more Quizzes Probability and Statistics in PDF only on Docsity! Quiz 6 Name: 1. An manufacturing plant produces lanterns. The mean length of time to pro- duce one lantern is 183 seconds, and the standard deviation is 28 seconds. The distribution is strongly right skewed. a) What is the probability that a random sample of 1500 lanterns has a mean production time of 184 seconds? Well, the correct answer is 0! The probability that a mean production time is 184 seconds is 0 in the sampling distribution, since it is just the area of a line segment. However, if the question were phrased ”What is the probability that a SRS sample of 1500 lanterns has a mean production time longer than 184 seconds”, we have to use the sampling distribution (We can use this because of the central limit theorem - 1500 is a large sample). So we compute the z-score for 184 in the sampling distribution. z = 184− 183 28/ √ 1500 = 1.38 Now we use table A to compute P (Z > 1.38). I get 8.38% on my calculator. b) Can you make a similar calculation and conclusion for an SRS of 3 lanterns? If you can, then do. If you can’t, explain why you can’t. You can’t, because the sample size is too small. The central limit theorem only applies when the sample size is large. IF THE POPULATION DISTRIBUTION were normal, then we could perform the calculation. 2. The results of a survey attempting to determine the average age at which Amer- icans marry appears in a survey. Explain what the following statement means: The .99-level confidence interval for µ is [23.56, 27.98]. It means that the probability of the mean age at which Americans marry being in [23.56, 27.98] is .99, or 99%.