Practice Exam. 1. What is the median of this data? A) 64 B) 63.5 C) 67.5 D) 59 E) 35

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1 Practice Exam Use the following to answer questions 1-2: A census is done in a given region. Following are the populations of the towns in that particular region (in thousands): 35, 46, 52, 63, 64, 71, 77, 82, and What is the median of this data? A) 64 B) 63.5 C) 67.5 D) 59 E) Which of the following is closest to the 30 th percentile for these data? A) 57.5 B) 63 C) 52.7 D) 53 E) 52 Use the following to answer questions 3-4: The number of bottles filled each day in a bottling plant is observed for a week: 674, 589, 613, 689, 554, 586, and Consider the data given above and find the mean. A) 585 B) 670 C) D) E) none of the above 4. Consider the sample data given above and find the standard deviation. A) 24 B) C) D) E) A car gets involved in an accident 80% of the time if it is defective. If it is not defective, the probability reduces to 40%. 30% of all cars are defective. If a car is involved in an accident, what is the probability that it was defective? A) 0.32 B) 0.24 C) D) 0.12 E) Use the following to answer questions 6-7: Two players are competing in a shooting gallery, each getting one shot at the target. The probability of the first shooter hitting the target is 0.57 and the probability of the second shooter hitting the target is 0.65.

2 6. What is the probability that both shooters hit their targets? A) 0.08 B) C) D) E) What is the probability that at least one of the two players hits the target? A) B) C) D) E) If the probability of A is 0.5 and the probability of B is 0.2 and the probability of the union of A and B is 0.7, then: A) A and B are independent B) A and B are mutually exclusive C) A and B are dependent D) A and B do have an intersection E) Impossible to determine Use the following to answer questions 9-10: The probability distribution for the delay in hours of the evening flight from Chicago to New York is as follows: x P(x) Find the expected delay in the flight. A) 3.7 B) 4.0 C) 1.0 D) Find the standard deviation of the flight delay. A) 2.00 B) 0.2 C) D) The probability of a person liking an advertisement is 0.6. Ten individuals are interviewed at random. What is the probability that exactly five like the advertisement? A) B) C)

3 D) A number very close to zero 12.From a group of four men and four women, a committee of four is to be chosen. What is the probability that this committee consists of exactly two men and two women? A) 1/10 B) 5/7 C) 1/14 D) 18/35 13.Find P(-2 < Z < 2). A) B) C) D) Fluctuations in the exchange rate of dollars against the pound sterling over a short time period were approximated by a normal distribution with a mean of 2.01 and a standard deviation of What is the probability that the rate on a particular day was more than 1.90? A) B) C) D) The weight of apples in a farm is normally distributed, with a mean of 110 grams, and a standard deviation of 15 grams. Find the probability that an apple selected at random will weigh between 95 and 105 grams. A) B) C) D) E) A bank has an average balance of $495 and a standard deviation of $102, in its checking accounts. What is the probability that 36 randomly selected accounts have an average balance greater than $500? A) B) C) D) E) Which of the following statements does not refer to the Central Limit Theorem? A) The expected value of the mean of the distribution of sample means is μ. B) The distribution of sample means is approximately normally distributed. C) The Central Limit Theorem is true for any distribution, when the sample size is at least 30. D) The standard deviation of the distribution of sample means is equal to σ. E) When a non-normal population is sampled, the distribution of sample means is still normally distributed, as long as the sample size is large.

4 18. A population has a mean of 90 and a standard deviation of 160. A random sample of 100 is selected. What is the standard error? A) 16 B) C) 1.5 D) A study was conducted to evaluate the stress level of senior business students at a particular college. Forty students were selected at random from the senior business class, and their stress level was monitored by attaching an electrode to the frontalis muscle (forehead). For the forty students, the mean EMG (electromyogram) activity was found to be 35.8 microvolts. In addition, the standard deviation of the EMG readings was found to be 2.5 microvolt. What would be the 99% confidence interval on the true mean EMG activity for all seniors in the class? A) [34.78, 36.82] B) [34.72, 36.78] C) [34.96, 36.52] D) [34.74, 36.05] E) [34.98, 36.51] 20. The mean of the sampling distribution of the sample mean is: A) equal to the mean of the population. B) an approximation of the mean of the population. C) not a good estimate of the population mean. D) equal to the population mean divided by n. E) none of the above. 21. For n = 25, sample mean = 645, and s = 55, construct a 99% confidence interval for the population mean. A) [614.23, ] B) [617.59, ] C) [617.67, ] D) [613.43, ] E) [616.68, ] 22. A credit card company wants to estimate the average balance of its customers. A random sample of 144 customers shows that the mean credit is $135, with a standard deviation of $43. Construct a 95% confidence interval for the mean balance. A) [127.98, ] B) [129.11, ] C) [129.06, ] D) [125.62, ] E) [128.25, ] 23. If the population standard deviation is not known, what should be used as a point estimate? A) The standard deviation of a few sample means. B) The sample mean. C) The sample standard deviation. D) Any of the above When is the t-distribution used in the construction of confidence intervals? A) When the population standard deviation is not known and the sample is small.

5 B) When the population standard deviation is known. C) Either the normal or t-distribution may be used. D) Always. E) For finite populations and large samples. 25. How much larger should the sample be if we want the confidence interval to be one tenth as wide as it is currently? A) 100 times B) 10 times C) 50 times D) 1000 times E) not enough information to determine 26. A 95% confidence interval for the population mean is [106, 116]. The width of a 99% confidence interval for the mean, based on this information, would be: A) 13.1 B) 22.5 C) 10 D) 5 E) Impossible to determine 27. If α =.05 for a two-tailed hypothesis test using the z test, the critical values are: A. ±1.90 B. ±1.96 C. ±2.00 D. ±2.33 E. ± The proportion of defective items is not allowed to be over 15%. A buyer wants to test whether the proportion of defectives exceeds the allowable limit. The buyer takes a random sample of 100 items and finds that 19 are defective. The conclusion is: A) Reject H 0. B) Can t reject H 0. C) Can t tell. 29. The proportion of defective items is not allowed to be over 15%. A buyer wants to test whether the proportion of defectives exceeds the allowable limit. The buyer takes a random sample of 100 items and finds that 19 are defective. State the null and alternative hypotheses for this test. A) H 0 : p.15, H 1 : p >.15 B) H 0 : p <.15, H 1 : p >.15 C) H 0 : p =.15, H 1 : p *.15 D) H 0 : p <.15, H 1 : p >.15 E) none of the above 30. I want to conduct a statistical test of whether or not the population mean is 150. My sample mean is 145, my sample standard deviation is 56, and my sample size is 100. The conclusion is: A) Can t reject H 0. B) Reject H 0. C) Can t tell.

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