Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Your answer 1 Final Exam - BUS322 E NAME: ________________________________________________________________ 1. Which of the following provides a measure of central location for the data? a. Standard deviation b. Mean c. Variance d. Range 2. The variance of a sample of 169 observations equals 576. The standard deviation of the sample equals a. 13 b. 24 c. 576 d. 28,461 3. The median is a measure of a. Relative dispersion b. Absolute dispersion c. Central location d. Relative location 4. The difference between the largest and the smallest data values is the a. Variance b. Interquartile range c. Range d. Coefficient of variation 5. The most frequently occurring value of a data set is called the a. Range b. Mode c. Mean d. Median 6. Which of the following symbols represents the standard deviation of the population? a. 2 b. c. d. 2 Exhibit 1 The following is the frequency distribution for the speeds of a sample of automobiles traveling on an interstate highway. Speed Miles per Hour 50 - 54 55 - 59 60 - 64 65 - 69 70 - 74 75 - 79 Total Frequency 2 4 5 10 9 5 35 7. Refer to Exhibit 1. The mean is a. 35 b. 670 c. 10 d. 67 8. Refer to Exhibit 1. The standard deviation is a. 6.969 b. 7.071 c. 48.570 d. 50.000 9. Suppose you independently flip a coin times and the outcome of each toss can be either head (with probability ) or tails (also with probability ). Denote by the number of times the outcome is tails (out of the tosses). The random variable has a: a. Bernoulli distribution b. Poisson distribution c. Binomial distribution d. Exponential distribution 10. The time between the arrival of one customer and the arrival of the next customer has an exponential distribution and is independent of previous arrivals. The number of customers that will arrive during the next hour has: a. A Poisson distribution b. A Gamma distribution c. An exponential distribution d. A binomial distribution 3 11. Traditionally, about 70% of students in a particular Statistics course at Lynn are successful. Suppose 20 students are selected at random from all previous students in this course. What is the probability that 15 of them will have been successful in the course? a. 0.7624 b. 0.2378 c. 1.2356 d. 0.4567 12. P (Z < -1.983), where Z is a standard normal random variable is closest to: a. 0.0237 b. 0.9763 c. 0.4763 d. 0.0559 13. If Z is a standard normal random variable, and P (Z > c) = 0.65, then the value of c is closest to: a. -0.2578 b. 0.2578 c. -0.3853 d. 0.3853 14. Mark is a high jumper. The height she can jump is normally distributed with a mean of 1.15 m and a standard deviation of 0.05 m. On 25% of her jumps, Mark clears h meters or more. What is the value of h? a. 1.12 meters b. 1.14 meters c. 1.16 meters d. 1.18 meters 15. A manufacturer wishes to ensure that 98% of the bolts that are produced from a manufacturing process have a diameter that lies within 0.05 mm of the mean. For this to be so, then the standard deviation of the process must be equal to: a. 0.0243 mm b. 0.0255 mm c. 0.0304 mm d. 0.0430 mm 16. Which of the following statements are true? a. The larger the sample size, the greater the sampling error b. The more categories or breakdowns you want to make in your data analysis, the larger the sample needed c. The fewer categories or breakdowns you want to make in your data analysis, the larger the sample needed d. As sample size decreases, so does the size of the confidence interval 4 17. ___________ is a set of elements taken from a larger population according to certain rules. a. Sample b. Population c. Statistic d. Element 18. Heights of college women have a distribution that can be approximated by a normal curve with a mean of 65 inches and a standard deviation equal to 3 inches. About what proportion of college women are between 65 and 67 inches tall? a. 0.75 b. 0.50 c. 0.25 d. 0.17 19. Suppose that vehicle speeds at an interstate location have a normal distribution with a mean equal to 70 mph and standard deviation equal to 8 mph. What is the zscore for a speed of 64 mph? a. 0.75 b. + 0.75 c. 6 d. + 6 20. The probability is p = 0.80 that a patient with a certain disease will be successfully treated with a new medical treatment. Suppose that the treatment is used on 40 patients. What is the "expected value" of the number of patients who are successfully treated? a. 40 b. 20 c. 8 d. 32 21. What Z-value is associated with a 95% confidence interval? a. 1.28 b. 1.65 c. 1.96 d. 2.58 22. What is the value of alpha for a 98% confidence interval? a. 0.20 b. 0.10 c. 0.05 d. 0.02 5 23. Suppose that you wish to obtain a confidence interval for a population mean. Under the conditions described below - The population is far from being normally distributed. - The sample size is large. Should you use the a. t-interval procedure b. z-interval procedure c. Neither 24. Suppose that you wish to obtain a confidence interval for a population mean. Under the conditions described below - The population standard deviation is unknown. - The population is normally distributed. - The sample size is small. Should you use the a. z-interval procedure b. t-interval procedure c. Neither 25. What is z value when = 0.05? a. 1.645 b. 2.575 c. 2.33 d. 1.96 26. A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval. a. We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. b. 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144. c. 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144. d. We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,04to $154,144. 27. A random sample of 72 statistics students was taken to estimate the proportion of students who also were in the Math Club. The 90% confidence interval was 0.438 to 0.642. Using this information, what size sample would be necessary to estimate the true proportion to within 0.08 using 95% confidence? a. 105 b. 150 c. 420 d. 597 6 28. A sample of 50 students was taken from the local university. These students spent an average of $170 on books this semester, with a standard deviation of $25.50. Which of the following could you say with 95% confidence was the average spent on books by these 50 students? a. $170 plus or minus $3.46 b. $170 plus or minus $5.95 c. $170 plus or minus $8.42 d. None of these is correct. 29. Fifteen SmartCars were randomly selected and the highway mileage of each was noted. The analysis yielded a mean of 47 miles per gallon and a standard deviation of 5 miles per gallon. Which of the following would represent a 90% confidence interval for the average highway mileage of all SmartCars? a. 47 1.753 5 / 15 b. 47 1.761 5 / 15 c. 47 1.345 5 / 15 d. 47 1.645 5 / 15 30.Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students. a. 89.08 < < 94.92 b. 87.27 < < 96.73 c. 87.29 < < 96.71 d. 87.77 < < 96.23 31. In hypothesis testing, the tentative assumption about the population parameter is a. The alternative hypothesis b. The null hypothesis c. Either the null or the alternative d. None of these alternatives is correct. 32. The p-value a. Is the same as the Z statistic b. Measures the number of standard deviations from the mean c. Is a distance d. Is a probability 33. In hypothesis testing if the null hypothesis is rejected, a. No conclusions can be drawn from the test b. The alternative hypothesis is true c. The data must have been accumulated incorrectly d. The sample size has been too small 7 34. The error of rejecting a true null hypothesis is a. A Type I error b. Type II error c. Is the same as d. Committed when not enough information is available 35. The level of significance in hypothesis testing is the probability of a. Accepting a true null hypothesis b. Accepting a false null hypothesis c. Rejecting a true null hypothesis d. None of these alternatives is correct 36. When the following hypotheses are being tested at a level of significance of H0: 100 Ha: < 100 The null hypothesis will be rejected if the p-value is a. b. > c. > /2 d. /2 37. A two-tailed test is performed at 95% confidence. The p-value is determined to be 0.09. The null hypothesis a. Must be rejected b. Should not be rejected c. Could be rejected, depending on the sample size d. Has been designed incorrectly Exhibit 2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. 38. Refer to Exhibit 2. The test statistic is a. 1.96 b. 1.64 c. 2.00 d. 0.056 8 39. Refer to Exhibit 2. The p-value is between a. .005 to .01 b. .01 to .025 c. .025 to .05 d. .05 to .10 40. Refer to Exhibit 2. At 95% confidence, it can be concluded that the mean of the population is a. Significantly greater than 3 b. Not significantly greater than 3 c. Significantly less than 3 d. Significantly greater then 3.18