Statistics for Business - Final Review Exam.

Statistics for Business - Final Review Exam A sample is the entire group of individuals or items being studied. True or False - Correct Answers: False The width of the class, can be determined by subtracting the lower limit of of a class from the lower limit of the next higher class. True or False - Correct Answers: True - we use the upper limit minus the lower limit. The upper limit of a class will be the lower limit of the next class. A data list will always have exactly one mean and exactly one mode. True or False - Correct Answers: False The quartiles divide data sets into four equal parts. True or False - Correct Answers: True To convert a frequency distribution to a relative frequency distributions, divide each class frequency by the sum of the class frequencies. True or False - Correct Answers: True A left skewed distribution is not symmetrical and the long tail is to the right. True or False - Correct Answers: False A parameter is a measurable characteristic of a sample. True or False - Correct Answers: False Extremely high or low values affect the value of the median and mode. True or False - Correct Answers: False For any distribution, there are an equal number of values above the mean and below it. True or False - Correct Answers: False The sample variance is roughly the mean of the sum of the squared differences between each observation and the median. True or False. - Correct Answers: False A data set has 80 observations. Using the 2 to the K rule, what is the number classes? - Correct Answers: 7 -- 2^7 is the first value that is above 80. 2^6 is only 64. A ---- is a bar graph in which the height of each rectangle is the frequency or relative frequency of the class/category. The width of each rectangle is the same, and the rectangles do not touch each other. - Correct Answers: Bar Chart After constructing any frequency distribution for a sample, what should be the sum of the frequencies. - Correct Answers: Sample size Which information can you obtain from a box plot but not from histogram? - Correct Answers: Largest and smallest values A group of 100 students were surveyed about their interest in a new International Studies program. Interest was measured in terms of high, medium, or low. 30 students responded high interest; 50 students responded medium interest, 20% students responded low interest. What is the type of the variable interest? - Correct Answers: Ordinal A histogram of a dataset indicates that the distribution of the data is skewed left, which measure of central tendency will likely be smaller, the mean or the median? - Correct Answers: Mean Find the sample standard deviation based on the following report from StatCrunch -- Variance is 4824.77278 - Correct Answers: The sample standard deviation is the square root of the variance which would be 69.46 The lifetime (in weeks) of a certain type of lightbulb is approximately bell-shaped, with mean 252 and standard deviation of 8. If one lightbulb from this distribution has a z-scores of +3, what is its lifetime? - Correct Answers: -2 and +1 The lifetime (in weeks) of a certain type of lightbulb is approximately bell-shaped, with mean 252 and standard deviation of 8. By using Empirical Rule, what percent of lightbulb has its lifetime between 236 and 260? - Correct Answers: 81.5% The lifetime (in weeks) of a certain type of lightbulb is approximately bell-shaped, with mean 252 and standard deviation of 8. By using Empirical Rule, what percent of lightbulb has its lifetime greater than 268? - Correct Answers: 2.5% Which measures of center are not affected by extremely small or extremely large values? - Correct Answers: Median and Mode The mean, as a measure of center would be the least appropriate for which of the following? - Correct Answers: Marital status of college students at a particular university. Rank the measures of spread in terms of their relative computational difficulty, from least to most difficulty. - Correct Answers: Range, IQR, Variance The following is a box plot for test 1 and test 2 of math 1065 The bottom one if for test 1. State the shape of the distribution for test 1 and test 2. - Correct Answers: Left skewed and right skewed. Probability is a measure of the likelihood of random phenomenon or chance behavior. True or False - Correct Answers: True A coin is tossed two times. The probability is 1/2 that both two tosses will result in a head face up. True or false - Correct Answers: False Two events E and F are disjoint, if the occurrence of event E in a probability experiment does not affect the probability of event F. True or False - Correct Answers: False To apply the special AND rule, the events must be disjoint. - Correct Answers: False the probability of two independent events, A and B, is computed as P(A and B) = P(A) x P(B). True or False - Correct Answers: True The complement rule states that the probability of an event not occurring is equal to one minus the probability of its occurrence. True or False - Correct Answers: True In the following Venn Diagram, event A and event B are disjoint. - Correct Answers: True A random variance is assigned numerical values based on the outcomes of an experiment. True or False - Correct Answers: True A discrete random variable can have only certain clearly separated values. True or False - Correct Answers: True A probability distribution of discrete random variable is a listing of possible numerical values that can occur by chance and their corresponding probabilities. True or False - Correct Answers: True The sample space of an experiment is S = {1,3,5,7,9,11,12,15}. If event E={1,3,5,7,9,15} and Event F={9,11,12,15}, list the outcomes in E OR F - Correct Answers: {1,3,5,7,9,11,12,15} The sample space of an experiment is S = {1,3,5,7,9,11,12,15}. If event E={1,3,5,7,9,15} and Event F={9,11,12,15}. suppose the outcomes are equally likely, what is the probability that event E and event F both occur? - Correct Answers: 2/8 If P(E)= 0.25 and P(F)=0.45. Find P(E OR F) if P(E AND F)= 0.25 - Correct Answers: P(E OR F)=0.45 A study by the National Park Service revealed that 70% of the vacationers going to the Rocky Mountain region visit Yellowstone Park, 40% visit the Grand Tetons and 35% visit both. What is the probability that a vacationer will visit at least one of these attractions? - Correct Answers: 0.75 A study by the National Park Service revealed that 70% of the vacationers going to the Rocky Mountain region visit Yellowstone Park, 40% visit the Grand Tetons and 35% visit both. What is the probability of a vacationer visiting yellowstone park? P(yellowstone|grand tetons) = - Correct Answers: 0.0875 There are 10 rolls of film in a box and 3 are defective. Two rolls are selected without replacement. What is the probability of selecting a defective roll followed by another defective roll? - Correct Answers: 1/15 or about 0.07 Derrek Lee of the Chicago Cubs had the highest batting average in the 2005 MLB season. His average was 0.35. So assume the probability of getting a hit is 0.35 for each time he batted. In a particular game assume he batted FIVE times. Denote X = number of hits that Derrek Lee made in that game. Is the random variable about a count of successes? And what is a success? - Correct Answers: Yes. Success is "hit" Derrek Lee of the Chicago Cubs had the highest batting average in the 2005 MLB season. His average was 0.35. So assume the probability of getting a hit is 0.35 for each time he batted. In a particular game assume he batted FIVE times. Denote X = number of hits that Derrek Lee made in that game. Is the predetermined number of trials being performed? What is a trail? And how many trials? - Correct Answers: Yes. Trial= batting. n=5 Derrek Lee of the Chicago Cubs had the highest batting average in the 2005 MLB season. His average was 0.35. So assume the probability of getting a hit is 0.35 for each time he batted. In a particular game assume he batted FIVE times. Denote X = number of hits that Derrek Lee made in that game. Is there a chance of success the same from trial to trial? What is the common success probability? - Correct Answers: Yes. p=0.35 Derrek Lee of the Chicago Cubs had the highest batting average in the 2005 MLB season. His average was 0.35. So assume the probability of getting a hit is 0.35 for each time he batted. In a particular game assume he batted FIVE times. Denote X = number of hits that Derrek Lee made in that game. Suppose the trails are independent, we can conclude that random variable has a binomial distribution. - Correct Answers: True. and n=5, p-0.35 Derrek Lee of the Chicago Cubs had the highest batting average in the 2005 MLB season. His average was 0.35. So assume the probability of getting a hit is 0.35 for each time he batted. In a particular game assume he batted FIVE times. Denote X = number of hits that Derrek Lee made in that game. Determine the probability of Derrek Lee missing all of them - Correct Answers: 0.116 Derrek Lee of the Chicago Cubs had the highest batting average in the 2005 MLB season. His average was 0.35. So assume the probability of getting a hit is 0.35 for each time he batted. In a particular game assume he batted FIVE times. Denote X = number of hits that Derrek Lee made in that game. What is the mean of X? - Correct Answers: 1.75 Derrek Lee of the Chicago Cubs had the highest batting average in the 2005 MLB season. His average was 0.35. So assume the probability of getting a hit is 0.35 for each time he batted. In a particular game assume he batted FIVE times. Denote y = number of misses that Derrek Lee had in that game. What is the standard deviation of Y? - Correct Answers: 1.0665 This year a special preparation course is offered, and 36 seniors planning to take the ACT test enrolled in the course. The mean of their 36 ACT scores is 22.1. Assume ACT scores vary normally with a standard deviation of 6. Find a 95% confidence interval of the mean ACT scores of seniors ( who took the special course ). This is a __________problem - Correct Answers: Z-problem This year a special preparation course is offered, and 36 seniors planning to take the ACT test enrolled in the course. The mean of their 36 ACT scores is 22.1. Assume ACT scores vary normally with a standard deviation of 6. Find a 95% confidence interval of the mean ACT scores of seniors ( who took the special course ) Select the closest answer from below - Correct Answers: (20.14, 24.06) This year a special preparation course is offered, and 36 seniors planning to take the ACT test enrolled in the course. The mean of their 36 ACT scores is 22.1. Assume ACT scores vary normally with a standard deviation of 6. Find a 95% confidence interval of the mean ACT scores of seniors ( who took the special course ). What is the margin of error of this 95% confidence interval? - Correct Answers: 1.96 This year a special preparation course is offered, and 36 seniors planning to take the ACT test enrolled in the course. The mean of their 36 ACT scores is 22.1. Assume ACT scores vary normally with a standard deviation of 6. Find a 95% confidence interval of the mean ACT scores of seniors ( who took the special course ). What is the critical value of this confidence interval? - Correct Answers: 1.96 This year a special preparation course is offered, and 36 seniors planning to take the ACT test enrolled in the course. The mean of their 36 ACT scores is 22.1. Assume ACT scores vary normally with a standard deviation of 6. Find a 90% confidence interval of the mean ACT scores of seniors ( who took the special course ). What is the critical value? - Correct Answers: 1.65 Statistics professors study on the average number of headaches when taking Math 2283. They sampled 11 students of Math 2283 at ECU, and obtained the following data: {1, 5, 11, 24, 7, 0, 9, 15, 6, 3, 33} Assume that the number of headaches of students in Math 2283 is normally distributed. To find a confidence interval of the mean number of headaches. This is a __________ problem - Correct Answers: T-interval Statistics professors study on the average number of headaches when taking Math 2283. They sampled 11 students of Math 2283 at ECU, and obtained the following data: {1, 5, 11, 24, 7, 0, 9, 15, 6, 3, 33} Assume that the number of headaches of students in Math 2283 is normally distributed. Find a 95% confidence interval of the mean number of headaches. - Correct Answers: (3.54, 17.18 Statistics professors study on the average number of headaches when taking Math 2283. They sampled 11 students of Math 2283 at ECU, and obtained the following data: {1, 5, 11, 24, 7, 0, 9, 15, 6, 3, 33} Assume that the number of headaches of students in Math 2283 is normally distributed. Find a 90% confidence interval of the mean number of headaches. - Correct Answers: (4.82, 15.91) Statistics professors study on the average number of headaches when taking Math 2283. They sampled 11 students of Math 2283 at ECU, and obtained the following data: {1, 5, 11, 24, 7, 0, 9, 15, 6, 3, 33} Assume that the number of headaches of students in Math 2283 is normally distributed. Find a 95% confidence interval of the mean number of headaches. What is the critical value of this confidence interval? - Correct Answers: 2.228 Statistics professors study on the average number of headaches when taking Math 2283. They sampled 11 students of Math 2283 at ECU, and obtained the following data: {1, 5, 11, 24, 7, 0, 9, 15, 6, 3, 33} Assume that the number of headaches of students in Math 2283 is normally distributed. Find a 90% confidence interval of the mean number of headaches. What is the critical value? - Correct Answers: 1.812 The sample means for a population that follows any distribution will also be normally distributed, regardless of the size of the samples. - Correct Answers: False, when population distribution is normal, the sample mean will follow a normal distribution, regardless of the size of the samples. When distribution is not normal, the sample mean will follow a normal distribution, only if the sample size is greater than or equal to 30. The positive critical value that corresponds to a 96% confidence t-interval with degress of freedom of 25 is1.825 - Correct Answers: False