AP STATS – Chapter 8 and 9 Test January 2010 Name ______________________ K ____/10 C ____/10 A ____/12 KNOWLEDGE 1. In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the probability that exactly 2 students have experienced math anxiety is (a) 0.3020 (b) 0.2634 (c) 0.2013 (d) 0.5 (e) 1 (f) None of the above 2. A factory makes silicon chips for use in computers. It is known that about 90% of the chips meets specifications. Every hour a sample of 18 chips is selected at random for testing. Assume a binomial distribution is valid. Suppose we collect a large number of these samples of 18 chips and determine the number meeting specifications in each sample. What is the approximate mean of the number of chips meeting specifications? (a) 16.20 (b) 1.62 (c) 4.02 (d) 16.00 (e) The answer cannot be computed from the information given. 3. In a large population, 46% of the households still own VCR’s. A simple random sample of 100 households is to be contacted and the sample proportion computed. The mean of the sampling distribution of the sample proportion is (a) 46 (b) 0.46 (c) About 0.46, but not exactly 0.46 (d) 0.00248 (e) The answer cannot be computed from the information given 4. If a population has a standard deviation , then the standard deviation of the mean of 100 randomly selected items from this population is (a) (b) 100 (c) /10 (d) /100 (e) 0.1 5. The distribution of values taken by a statistic in all possible samples of the same size from the same population is (a) The probability that the statistic is obtained (b) The population parameter (c) The variance of the values (d) The sampling distribution of the statistic (e) None of the above. The answer is . 6. Assume 13% of people are left-handed. If we select 5 people at random, find the probability for the outcomes described below:  a) The first lefty is the 5th person chosen. b) There is more than one lefty in the group. c) The first lefty is the 2nd or 3rd person chosen. d) There are exactly 3 lefties in the group. e) There are no more than 3 lefties in the group. COMMUNICATION 7. Suppose that you and your lab partner flip a coin 20 times and you calculate the proportion of tails to be 0.8. Your partner seems surprised at these results and suspects that the coin is not fair. Write a brief statement that describes why you either agree or disagree with him. Your response should relate to the principles of the course.  8. Suppose that each of the 25 students in a statistics class collects a random sample of 50 cans and calculates the mean number of ounces of soda.  a) Describe the approximate shape of the distribution for these 25 values of x . b) What important principle that we studied is used to answer the previous question? c) Can you calculate the probability that a single randomly selected can contains 11.9 ounces or less? If so, do it. If not, explain why you cannot. APPLICATION/COMMUNICATION 9. A certain beverage company is suspected of underfilling its cans of soft drink. The company advertises that its cans contain, on the average, 12 ounces of soda with standard deviation 0.4 ounce. Compute the probability that a random sample of 50 cans produces a sample mean fill of 11.9 ounces or less. (A sketch of the distribution is required.) [4/4] APPLICATION 10. A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales with the additional revenue going to education. Let p denote the proportion in the sample that says they support the increase. Suppose that 40% of all adults in Ohio support the increase.  a) If p is the proportion of the sample who support the increase, what is the mean of p ? ö ö b) What is the standard deviation of p ? ö c) Explain why you can use the formula for the standard deviation of p in this setting. ö d) Check that you can use the normal approximation for the distribution of p . ö e) Find the probability that p takes a value between 0.37 and 0.43. ö f) How large a sample would be needed to guarantee that the standard deviation of p is no ö more than 0.01? Explain.
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