midterm2solutions-101

# midterm2solutions-101 - STAT 200 Midterm (Time: 50 minutes,...

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STAT 200 Midterm Exam II (Section 101) (Time: 50 minutes, Friday, November 10, 2006, 9:00 - 9:50am) Name: Student ID: This exam is to be done with closed notes/books. One "cheat sheet" (8.5' x 11', two sided) is allowed. There are 5 problems, with a total of 100 points. Make sure you write your name and student [D. We prefer short answers without omitting key steps - you must show the key steps for Problems 3 - 5. Problem 1 (15 pts). Circle the correct answer: true (T) or false (F). (1) 'vVemust know the approximate distribution of a statistic, which is used to estimate a pop- ulation mean, in order to computer a confidence interval for that population mean. (!) F (2) A t-distribution with small degree of freedom has heavier tails than the standard normal distribution, but when the d~ee of freedom is large a t-distribution is very similar to the stan- dard normal distribution. l!J F (3) Since there is sampling error in estimation, the sampling distrib~n has a standard de- viation which is larger than the population standard deviation. T <!.J (4) If population, II has a larger true mean than population I, the sa~ mean from popu- lation II must be larger than the sample mean from population 1. T \!.) (5) If a test is significant at 5% level, the probability of Ho being true is 0.05. Problem 2 (36 pts). Circle the answer which is the closest to the correct answer (please choose only one answer). (1). An engineer designs an improved light bulb. The previous design had an average life- time of 1200 hours. The new bulb had a lifetime of 1201 hours, using a sample of 2000 bulbs. Although the difference is quite small, the effect was statistically significant. The explanation is ~ that new designs typically have more variability than standard designs. b) that the sample size is very large. c that the mean of 1200 is large. d) all of the above. (2) A simple random sample of size n is taken from a population with mean 10 and standard deviation 5. If weuse o~ half the sample, the mean of the sampling distribution of x would be a) 5 b) 10/0. (0to d) 2Jn/2 (3) The time it takes for a battery to fail is often not normally distributed. We select a simple random sample of 1000 batteries and compute the average of all the failure times. The sampling distribution of this average may be approximated b~ a) Binomial distribution b) uniform distribution 0normal distribution d) t distribution

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(4). An agricultural researcher plants 25 plots with a new variety of corn. The average yield for
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## This note was uploaded on 05/09/2011 for the course STAT 200 taught by Professor Karim during the Spring '08 term at The University of British Columbia.

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midterm2solutions-101 - STAT 200 Midterm (Time: 50 minutes,...

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