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AP Statistics Quiz C – Chapter 18 – Key 1. It is generally believed that nearsightedness affects about 12% of children. A school district gives vision tests to 133 incoming kindergarten children. a. Describe the sampling distribution model for the sample proportion by naming the model and telling its mean and standard deviation. Justify your answer. We can assume these kids are a random sample of all children, and certainly less than 10% of them. We expect np = 133(0.12) = 15.96 successes and 117.04 failures so the sample size is large enough to use the sampling model N(0.12, 0.028). b. Sketch and clearly label the model. c. What is the probability that in this group over 15% of the children will be found to be nearsighted? 0.15 − 0.12 = 1.07 0.028 P( pˆ > 0.15) = P(z > 1.07) = 0.142 z= 2. Wildlife scientists studying a certain species of frogs know that past records indicate the adults should weigh an average of 118 grams with a standard deviation of 14 grams. The researchers collect a random sample of 50 adult frogs and weigh them. In their sample the mean weight was only 110 grams. One of the scientists is alarmed, fearing that environmental changes may be adversely affecting the frogs. Do you think this sample result is unusually low? Explain. We have a random sample of frogs drawn from a much larger population. With a sample of size 50 the CLT says that the approximate sampling model for sample means will be N(118, 1.98). A sample mean of only 110 grams is about 4 standard deviations below what we expect, a very unusual result. 18-22 Copyright 2010 Pearson Education, Inc.