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MATH 264 QUIZ # 5 December 26, 2002 ANSWERS 1) When we calculate a z-score in an application of the central limit theorem we use the formula: a) z = x̄ − µ σ b) z = x − µx̄ σx̄ c) z = x̄ − µx̄ σx̄ " d) z = x−µ σ 2) The standard deviation of the sampling distribution of x̄ is deviation of the population. a) greater than c) equal to the standard b) greater than or equal to d) less than " 3) The mean weight of the students in a certain school is 80 k.g. and the standard deviation is 5 k.g. The probability that the mean weight of a sample of 100 students is greater than 81 k.g. is: (Below F (z) denotes the area under the standard normal curve from 0 to z.) a) 0.5 − F (2.5) b) 0.5 + F (2) c) 0.5 − F (2) " d) 0.5 + F (2.5) 4) When we sample from an infinite population, the standard error of the mean is multiplied when we increase the sample size from 16 to 25 by a factor of a) 16 25 b) 25 16 c) 4 5 " d) 5 4 5) Which of the following is true for the central limit theorem1 ? a) It cannot be used if the population being sampled has a binomial distribution. b) It can never be applied if n < 30. c) It can be used for finite populations provided that n is small and n/N is large. d) It can be used for finite populations provided that n is large and n/N is small. " 6) A random sample of size 64 is selected from a population of size 100000 and standard deviation is 5. The standard error of the mean is: a) 64 20000 b) 20000 64 c) 8 5 d) 5 8 " 7) When the population being sampled has a normal distribution, the central limit theorem can be applied: a) for n ≥ 30 c) for n ≤ 0.05 · N b) for n ≥ 0.05 · N d) for any n " 8) The probability of selecting a random sample of size 3 from a population of size 12 is: a) 1/220 " b) 1/1320 c) 220 d) 1320 9) It is impossible to apply the central limit theorem if the population does not follow a normal distribution. 1 Here and in what follows N denotes the population size. TRUE FALSE " 10) In order to apply the central limit theorem, n must be larger if the population being sampled has an unusual distribution. TRUE " FALSE 11) A simple random sample from a finite population is a sample which is chosen in such a way that each possible sample has the same probability of being selected. TRUE " FALSE 12) The finite population correction factor is omitted in situations where n constitutes only a small proportion of the population. TRUE " FALSE 13) A sample can be either finite or infinite. TRUE FALSE " 14) The standard deviation of the sampling distribution of the mean does not depend on the sample size involved. TRUE FALSE " 15) Sampling with replacement from a finite population is, in effect, sampling from an infinite population. TRUE " FALSE 2