QMB 3200 Final Exam 2025

Suppose we have the following data: 12, 17, 13, 25, 16, 21, 30, 14, 16, and 18. To find the 10% trimmed mean, what numbers should be deleted from the calculation? - Correct Answer-12 and 30 Which of the following is not resistant to the outliers in a data set? a. Median b. Mean c. Variance d. Interquartile range - Correct Answer-b. mean The pth percentile is a value such that at least p percent of the observations are: - Correct Answer-less than or equal to this value. Which of the following provides a measure of central location for the data? a. Mean b. Variance c. Mode d. Standard deviation - Correct Answer-a. mean When testing water for chemical impurities, results are often reported as BDL, that is, below detection limit. The following data set gives the measurements of the amount of lead in a series of water samples taken from inner-city households (ppm): 5, 7, 12, BDL, 10, 8, BDL, 20, 6 Which of the following is correct? a. The mean lead level in the water is about 10 ppm. b. The median lead level in the water is 8 ppm. c. The mean lead level in the water is about 8 ppm. d. The median lead level in the water is 7 ppm. - Correct Answer-d. The median lead level in the water is 7 ppm. A student made scores of 85, 56, and 91 on her first three statistics tests. What score does she need to make on her next test to have an 80 test average? - Correct Answer 88 Growth factors for the population of Dallas in the past five years have been 1, 2, 3, 4, and 5, respectively. The geometric mean is: - Correct Answer-^5square root 120 A sample of 99 distances has a mean of 24 feet and a median of 21.5 feet. Unfortunately, it has just been discovered that an observation that was erroneously QMB 3200 QMB 3200 recorded as "30" actually had a value of "35." If we make this correction to the data, then: - Correct Answer-the median remains the same, but the mean is increased. A numerical value used as a summary measure for a sample, such as sample mean, is known as a: - Correct Answer-sample statistic. The measure of location that is most likely to be influenced by extreme values in a data set is the: - Correct Answer-mean A student was performing an experiment that compared a new high protein food to the old food for pigs. He found the mean weight gain for subjects consuming the new food to be 12.8 pounds with a standard deviation of 3.5 pounds. Later, he realized that the scale was out of calibration by 1.5 pounds (meaning that the scale weighed items 1.5 pounds more). What should be the summary measures, mean and standard deviation, for the subjects consuming the new food? - Correct Answer-The mean should be 11.3 and the standard deviation should remain unchanged. When a set of data has suspect outliers, which of the following is the referred measure of central tendency? - Correct Answer-median In a sample of 500 students whose mean height is 67.8 inches, 150 were women. If the mean height of the women was 63.0 inches, what is the mean height of the men in the sample? - Correct Answer-69.9 The coefficient of variation formula - Correct Answer-the standard deviation divided by the mean and multiplied by 100. The summary statistics for the hourly wages of a sample of 130 system analysts are given below: Mean = 60 Range = 20 Mode = 73 Variance = 324 Median = 74 The coefficient of variation is equal to: - Correct Answer-(square root 324/ 60 x100)= 30% If the variance of a data set is correctly computed with the formula using in the denominator, which of the following is true? a. The data set is a population. b. The data set is adjusted for skewness. c. The data set is too small. d. The data set is a sample. - Correct Answer-d. The data set is a sample. QMB 3200 QMB 3200 In a sample of size five, the mean is 23 and four of the observations have the following deviations from the mean: -6, 2, 5, and 3. What is the value of the fifth observation? - Correct Answer--4 There are three executives in an office with age 56, 57, and 58. If a 57-year-old executive enters the room, then: - Correct Answer-the mean age will stay the same, but the variance will decrease. The difference between the largest and the smallest data values is the: - Correct Answer-range The interquartile range is: - Correct Answer-the difference between Q3 and Q1, the third and first quartiles. The standard deviation of a sample was reported to be 20. The report indicated that Σ (xi-x̄ )^2 = 7200. What is the sample size? - Correct Answer-20-1 = 19 The numerical value of the standard deviation can never be: - Correct Answer-negative The interquartile range is used as a measure of variability to overcome the fact that the: - Correct Answer-range is comprised of extreme values. Given the following information: Standard deviation = 8 Coefficient of variation = 64% The mean is - Correct Answer-8 / 64%= 12.5 The sum of deviations of the individual data elements from their mean is: - Correct Answer-always equal to zero The correlation coefficient ranges between: - Correct Answer--1 and 1 A numerical measure of linear association between two variables is the: - Correct Answer-covariance A doctor records a pair of information (temperature when admitted, temperature 24 hours later) for 400 hospital patients selected at random. He finds that the average patients' temperature upon admission is 101 degrees and 99 degrees 24 hours later. The standard deviation is 1.5 degrees for temperatures when admitted and .5 degrees 24 hours later. The correlation between the two temperatures is .8. What is the covariance between the variables? - Correct Answer-Σ (xi-x̄ )(yi- ȳ)/n-1= .60 Suppose the correlation coefficient rxy between the amount of sleep (in hours) "x" and number of yawns made in 8:00 a.m. classes "y" of 100 business statistics students is computed to be -.82. Then: - Correct Answer-the least squares line slopes downward. QMB 3200 QMB 3200 what statistic measures both the strength and direction of a linear relationship? - Correct Answer-correlation coefficient Positive values of covariance indicate: - Correct Answer-a positive relation between the independent and the dependent variables. The correlation coefficient is: - Correct Answer-a number between -1 and 1 inclusive that measures the strength and direction of the linear relationship between two numerical variables. The correlation coefficient between two scores X and Y equals .80. If both the X scores and the Y scores are converted to z-scores, then the correlation between the z-scores for X and the z-scores for Y would be: - Correct Answer-.80 In a standard normal distribution, what z-score corresponds to the 75th percentile? - Correct Answer-z = .67 The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What is the percentage that, if driven normally, the car will get 100 miles per gallon? - Correct Answer-100-75/10 = 2.5 The corresponding z score is .6% A normal distribution with a mean of zero and a standard deviation of one is called: - Correct Answer-a standard normal probability distribution. A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1500 steps. How many steps would he have to take to make the cut for the top 5% for his distribution? - Correct Answer-To be at the top 5% of his distribution, he would need a z-score of 1.645. This equates to taking 12,467 steps Suppose that a basketball player scored, on average, 15 points per game. Also suppose that the distribution of points scored by this player was normal. If he scores 20 points or more 4.78% of the time, what is his standard deviation? - Correct Answer-100 4.78= 95.22 percentile, corresponding z score is 1.66 20-15= 5 5/1.66= 3 For the standard normal probability distribution, the area to the left of the mean is: - Correct Answer-.50 In a standard normal probability distribution, the mean is located at the center of the, curve which means that half of the area is below the mean and half is above the mean QMB 3200 QMB 3200 If z is a standard normal random variable, then compute P(z -1.75). - Correct Answer Using a standard normal table, P(z -1.75) = .96. The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What value represents the 50th percentile of this distribution? - Correct Answer-The 50th percentile of a normal distribution is located at its mean = 75 The center of a normal curve is: - Correct Answer-the mean of the distribution. If z is a standard normal random variable, then compute P(-1.5 z 1.5). - Correct Answer-Using a standard normal table, P(-1.5 z 1.5) = .87. A negative value of z indicates that: - Correct Answer-the number of standard deviations of an observation is below the mean. A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1500 steps. One day he took 15,000 steps. What was his percentage of steps that day? - Correct Answer-/1500= 3.33 The z-score for 15,000 steps is z = 3.33. P(z ≤ 3.33) = 99.96% A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1500 steps. What percent of the time will he exceed 13,000 steps? - Correct Answer-/1500= 2 The z-score for 13,000 steps is z = 2. P(z ≥ 2) = 2.28% Which of the following is not a characteristic of the normal probability distribution? a. The distribution is symmetrical. b. The mean of the distribution can be negative, zero, or positive. c. The standard deviation must be one. d. The mean, median, and mode are equal. - Correct Answer-c. The standard deviation must be one. Parameters are: - Correct Answer-numerical characteristics of a population When drawing a sample from a population, the goal is for the sample to: - Correct Answer-match the targeted population. For a(n) _____ , it is impossible to construct a sampling frame. - Correct Answer-infinite population Which of the following is not a symbol for a parameter? - Correct Answer-s QMB 3200 QMB 3200 A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is .22 ounces. In this problem, the value .22 ounces is: - Correct Answer-a parameter. Which of the following is(are) true? I. The mean of a population depends on the particular sample chosen. II. The standard deviations of two different samples from the same population may be the same. III. Statistical inferences can be used to draw conclusions about the populations based on sample data. - Correct Answer-II and III A simple random sample of size n from an infinite population is a sample selected such that each element is selected ____________ and is selected from the same _____________ - Correct Answer-independently, population. A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have: - Correct Answer-the same probability of being selected. A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size: - Correct Answer-n has the same probability of being selected. How many simple random samples of size 5 can be selected from a population of size 8? - Correct Answer-8!/5!(8-5)!= 56 There are 6 children in a family. The number of children defines a population. The number of simple random samples of size 2 (without replacement) that are possible is equal to: - Correct Answer-6!/2!(6-2)! The medical director of a company looks at the medical records of all 50 employees and finds that the mean systolic blood pressure for these employees is 126.07. The value of 126.07 is: - Correct Answer-a parameter The sample statistic characteristic s is the point estimator of: - Correct Answer-σ Which of the following is a point estimator? - Correct Answer-s The value of the _____ is used to estimate the value of the population parameter. - Correct Answer-sample statistic The sample mean is the point estimator of: - Correct Answer-μ Sample statistics, such as x ̅ , s, or p ̅ , that pr