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introduction to statistical investigations

Questions and Answers of Introduction To Statistical Investigations

ShirtCo would like to know the total amount spent by each of its customers on each of its products during each of the years from 1995 through 1998. Using the database given in the file P4_25.MDB,
ShirtCo would also like to know the proportions sold through each channel (i.e., wholesale versus retail) for each of its products during each quarter of the years from 1995 through 1998. Using the
The Fine Shirt Company would like to know what proportion of each customer’s total dollar purchases in 1999 came from buying Short-sleeve Seersucker shirts. Furthermore, it would like to compare
ShirtCo is trying to determine who was its biggest customer, as measured by total units sold, in 1998. Once ShirtCo determines which customer was responsible for the maximum level of total unit
A corporate executive officer is attempting to arrange a meeting of his three vice presidents for tomorrow morning. He believes that each of these three busy individuals, independently of the others,
Several students enrolled in a finance course subscribe to Money magazine. If two students are selected at random from this class, the probability that neither of the chosen students subscribes to
You have placed 30% of your money in investment A and 70% of your money in investment B. The annual returns on investments A and B depend on the state of the economy as shown in Table 5.35. Determine
There are three possible states of the economy during the next year (states 1, 2, and 3). The probability of each state of the economy, as well as the percentage annual return on IBM and Disney
There are three possible states of the economy during the next year (states 1, 2, and 3). The probability of each state of the economy, as well as the percentage annual return on P&G and US
The annual returns on stocks 1 and 2 for three possible states of the economy are given in Table 5.42. a. Find and interpret the correlation between stocks | and 2. b. Consider another stock
Wal-Mart buyers seek to purchase adequate supplies of various brands of toothpaste to meet the ongoing demands of its customers. In particular, Wal-Mart is interested in estimating the proportion of
Warren Dinner has invested in nine different investments. The returns on the different investments are probabilistically independent, and each return follows a normal distribution with mean $500 and
Consider a frame consisting of 500 households in a middle-class neighborhood that was the recent focus of an economic development study conducted by the local government. The data are in the file
The manager of a local supermarket wants to know the average amount (in dollars) customers spend at his store on Fridays. He would like to study the buying behavior of each customer who makes a
The manager of a local supermarket wants to know the average amount (in dollars) customers spend at his store on Fridays. He would like to study the buying behavior of each customer who makes a
Auditors of a particular bank are interested in comparing the reported value of customer savings account balances with their own findings regarding the actual value of such assets. Rather than
The manager of a local supermarket wants to estimate the average amount customers spend at his store on Fridays. He would like to study the buying behavior of each customer who makes a purchase at
The Hite Report was Sheri Hite’s survey of the attitudes of American women toward sexuality. She sent out over 100,000 surveys; each contained multiple-choice and open-ended questions. These
Repeat Problem 65, but now stratify the consumers in the given frame by age rather than by gender. How does this modification affect your answers to the questions posed in parts b and c? Finally,
Wal-Mart buyers seek to purchase adequate supplies of various brands of toothpaste to meet the ongoing demands of their customers. In particular, Wal-Mart is interested in knowing the proportion of
Suppose that you are an entrepreneur interested in establishing a new Internet-based sports information service. Furthermore, suppose that you have gathered basic demographic information on a large
Continuing the previous problem, suppose that SteelCo can pay money to reduce the standard deviation of the process. It costs e100D dollars to reduce the standard deviation from 0.025 to 0.025 — d.
Suppose that 60% of all people prefer Coke to Pepsi. We randomly choose 500 people and ask them if they prefer Coke to Pepsi. What is the probability that our survey will (erroneously) indicate that
Consider again SweetTooth Candy Company’s decision problem described in Problem 1. Use the PrecisionTree add-in to identify the strategy that minimizes SweetTooth’s expected cost of meeting its
Consider again Carlisle Tire and Rubber’s decision problem described in Problem 2. Use the PrecisionTree add-in to identify the strategy that maximizes this tire manufacturer’s expected profit.
Consider again the landowner’s decision problem described in Problem3. Use the Precision Tree add-in to identify the strategy that maximizes the landowner’s expected net earnings from this
The lifetime of a washing machine is normally distributed with mean 4 years. Only 15% of all washing machines last at least 5 years. What is the standard deviation of the lifetime of a washing
You have been told that the distribution of regular unleaded gasoline prices over all gas stations in Indiana is normally distributed with mean $1.25 and standard deviation $.075, and you have been
Suppose that the number of ounces of soda put into a Pepsi can is normally distributed with jt = 12.05 ounces and o = 0.03 ounce. a Legally, acan must contain at least 12 ounces of soda. What
Suppose that 52% of all registered voters prefer Bill Clinton to Bob Dole. (You may substitute the names of the current presidential candidates!) a Inarandom sample of 100 voters, what is the
A lightbulb manufacturer wants to estimate the number of defective bulbs contained in a typical box shipped by the company. Production personnel at this company have recorded the number of defective
The employee benefits manager of a small private university would like to estimate the proportion of full-time employees who prefer adopting the first (i.e., plan A) of three available health care
A manufacturing company’s quality control personnel have recorded the proportion of defective items for each of 500 monthly shipments of one of the computer components that the company produces.
A finance professor has just given a midterm examination in her corporate finance course. In particular, she is interested in learning how her large class of 100 students performed on this exam. The
Consider a frame consisting of 500 households in a middle-class neighborhood that was the recent focus of an economic development study conducted by the local government. The data are in the file
A real estate agent has received data on 150 houses that were recently sold in a suburban community. Included in this data set are observations for each of the following variables: the appraised
Consider the average time (in minutes) it takes citizens of each of 325 metropolitan areas across the United States to travel to work and back home each day. The data are in the file P2_11.XLS. Use
Find a 95% confidence interval for the mean total cost of all customer orders. Then do this separately for each of the four regions. Create side-by-side boxplots of total cost for the four regions.
Find a 95% confidence interval for the mean amount of all Rebco’s bills. Do the same for each customer size separately.
Find a 95% confidence interval for the mean number of days it takes Rebco’s customers (as a combined group) to pay their bills. Do the same for each customer size separately. Create a boxplot for
The following probability distribution represents the payout for a game. Suppose $2 is added to all the payouts. How would the mean and standard deviation change from those of the original
Omega-3 fatty acids are essential to the function of the human body, with evidence suggesting that they help lower the risk of heart disease and other blood disorders through their role in
Researchers Dumas and Dunbar wanted to see whether stereotypes related to creativity can influence a subject’s creativity. The 96 subjects were randomly placed into three groups of 32 each. One
Similar to Exercise 9.2.33, researchers Dumas and Dunbar wanted to compare the creativity of students with different majors at their university, specifically biology, physics, art, and theater. As a
The New England Journal of Medicine (Li et al., 2012) published a study investigating the effects of tai chi on postural stability in patients with Parkinson’s disease. Parkinson’s disease causes
Suppose you are flipping two fair coins and you are interested in the probability of getting at least one head. Which of the following is the sample space for this experiment? A. 3/4 B. P(H
Reconsider Exercise 11.8.1 where we assumed the proportion of all American citizens who have a valid passport is 0.46. Suppose again that a random sample of 100 Americans is to be taken and the
In the following probability distribution, what is P(X > 2)? A. 0.10 B. 0.30 C. 0.40 D. 0.50 E. 0.60 X 1 p(x) 0.40 2 0.10 3 0.30 4 0.20
Suppose that a U.S. adult is selected at random. What do you expect for the probability that the adult is a male? A. Close to zero B. Close to one-fourth C. Close to one-half D.
In rolling a fair six-sided die once, the event of getting a 2 and the first roll and the sum of 4 for both rolls are: A. Independent. B. Disjoint.C. Neither independent nor
Suppose you are spinning a cash prize wheel in which you have a 25% chance of winning a prize, as described in Exercise 11.6.1. Most prizes are fairly small values like $1 or $5, but one spot on the
Suppose heights from a certain population are normally distributed and you determine that the standardized statistic for someone’s height from that population is 1.56. What does that number
What is the mean outcome (expected value) in the probability distribution in Exercise 11.4.2?A. 0.20 B. 0.25 C. 2.3 D. 2.5 E. 2.6Data from Exercise 11.4.2In the following
The intersection of events A and B is when: A. P(A and B) = 1. B. P(A and B) = 0. C. Either A or B occurs. D. Both A and B occur at the same time. E. Either A or B occurs,
We can use simulations to: A. Get exact theoretical probabilities. B. Approximate probabilities fairly precisely. C. Get a very rough idea as to the value of a probability, but not at
Reconsider Exercise 11.8.2 where we assumed the proportion of all American citizens who have a valid passport is 0.46. Suppose again that a random sample of 100 Americans is to be taken and the
How would the mean and standard deviation change from those of the original distribution? A. They both would be multiplied by 2.B. The mean would be multiplied by 2, but the standard deviation
Suppose that a U.S. adult is selected at random. What do you expect for the probability that the adult is a member of Congress? A. Close to zero B. Close to one-fourth C. Close to
In rolling a fair six-sided die twice, the event of getting a 2 on the first roll and a sum of 12 for both the dice are: A. Independent. B. Disjoint. C. Neither independent nor
The following probability distribution represents payouts for spinning two different prize wheels, X and Y. Suppose a player gets to first spin wheel X and then wheel Y. What is the mean payout for
Suppose people in your town are being surveyed about shopping habits. Which one of the following situations is best modeled by a binomial model? A. You ask residents of your town, “Do you shop
Heights of a certain population are normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. We can say that about 95% of all heights in the population are: A.
The complement of event A is when: A. P(A) = 0. B. P(A) = 1. C. A does not occur. D. A occurs. E. A is very polite.
The probability of an event is: A. The number of outcomes in the sample space divided by the number of outcomes in the event only if the outcomes in the event are equally likely. B. The
What is the standard deviation of the outcome in the probability distribution in Exercise 11.4.2? A. 1.06 B. 1.19 C. 1.20 D. 1.41 E. 1.45Data from Exercise 11.4.2In the
Suppose that a U.S. adult is selected at random. What do you expect for the conditional probability that the adult is a member of Congress, given that he is male?A. Close to zeroB. Close to
For two events A and B, P(A) = 0.80, P(B) = 0.20, and P(A and B) = 0.16. It follows that A and B are: A. Independent but not disjoint. B. Both disjoint and independent. C. Neither
What is the difference between a binomial model and a geometric model? A. The geometric model doesn’t have binary (success or failure) outcomes, whereas a binomial model does. B. The
Recall Exercise 11.5.3 about spinning both wheels. What is the standard deviation of the distribution of payouts when a player gets to spin both wheels? A. 2.206 B. 4.413 C.
Suppose heights of a certain population are normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. What is the 80th percentile of this distribution? A. 70
When a normal distribution is used to calculate probabilities about the distribution of a sample proportion, it gives: A. Exact results. B. Exact results for large sample sizes and
When does P(A or B) = P(A) + P(B)? A. Always. B. Never. C. When events A and B occur at the same time. D. When events A and B are complements of each other. E. When events A
Suppose you want to simulate the probability that a family of six children will have at least two boys. You assume the probability of having a boy or a girl is the same. (Both are 1/2.) To start the
Suppose that a U.S. adult is selected at random. What do you expect for the conditional probability that the adult is a male, given that he or she is a member of Congress? A. Close to
Which of the probability distributions A–E is correct, where X = the number of heads when 3 fair coins are flipped? A.B.C.D.E. 0 p(x) 1/4 x 1 1/4 2 3 1/4 1/4 لیا
A classic probability problem is called the collector’s problem. For example, suppose that cereal boxes contain one prize each, with a total of four prizes to be collected. Also suppose that each
If two events, A and B, are independent, then which of the following must be true? (There may be more than one correct answer.) A. Events A and B will never occur at the same time. B.
Which of the following Venn diagrams correctly represents the situation in which P(A) = 0.20, P(B) = 0.30, and P(A and B) = 0.10? A.B.C.D.E. 0.10 0.10 0.50 0.20 B
Which of the two following scenarios would be better modeled with a binomial distribution? Explain your reasoning. A. Your high school has 3,200 students consisting of 50% males and 50% females.
Heights of a certain population are normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. The middle 50% of all the heights lie approximately between what two
Suppose a population consists of 10% left-handers. Which is more unlikely, getting more than 12% left-handers in a random sample of 100 people from this population or getting more than 12%
An event is: A. A collection of outcomes in a sample space B. Another word for sample space. C. The probability something will occur. D. The number of outcomes. E. How many
Reconsider Exercise 11.8.22, but with different sample sizes. Determine the probability that Karen grades a random sample of five exams in less total time than it takes John to grade a random sample
One estimate says that 46% of all Americans citizens have a valid passport. Suppose this is true exactly. Also suppose we wanted to randomly sample 100 Americans and find the proportion in our sample
Which of A–E is a valid probability distribution? A.B.C.D.E. 1 p(x) 0.30 2 0.20 3 0.30
If two events, A and B, are mutually exclusive, then which of the following must be true? (There may be more than one correct answer.) A. Events A and B will never occur at the same
Heights of a certain population are normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. What is the standardized statistic (z-score) for a person with a height of 66
Suppose you are spinning a cash prize wheel in which you have a 25% chance of winning a prize. Most prizes are fairly small values like $1 or $5, but one spot on the wheel is worth $100. In which one
In rolling a fair six-sided die twice, the event of getting a 2 on the first roll and the event of getting a 4 on the second roll are: A. Independent. B. Disjoint. C. Neither
In a survey of 106 college students, data were gathered on the number of piercings each student had and the number of classes they had skipped in the past 3 weeks. We want to determine whether there
According to the U.S. Census Bureau, 74.8% of households in the United States had home Internet access in 2012. a. Suppose 10 households in the United States are randomly chosen; what is the
Suppose two fair 4-sided dice (yes, they do exist) with sides labeled 1, 2, 3, and 4 are tossed. a. List the sample space of all possible outcomes. b. Let X represent the sum of the
A regular six-sided die is a cube on which each side shows a different number of dots (1 to 6). The table shown below gives the probabilities of the sums of the dots on two regular six-sided dice
The distribution of IQs is said to have a mean of 100 and a standard deviation of 15. Suppose a company was selling IQ+ pills so that those that took it would magically have their IQs transformed by
Suppose that you encounter two traffic lights on your drive to school. From past experience, you judge that the probability is 0.45 that the first light will be red when you get to it, 0.35 that the
If adult male gerbil weights are normally distributed with a mean of 95 grams and a standard deviation of 10 grams, using the empirical rule, what proportion of adult male gerbils weigh: a.
Given that P(A) = 0.40, P(B) = 0.50, and P(A and B) = 0.20, answer the following questions. a. What is P(A|B)? b. What is P(B|A)? c. What is P(A or B)? d. Are events A and B
In 2014, the U.S. Census Bureau estimated that 13% of U.S. residents were foreign-born. Suppose this is exactly true. If a random sample of 500 Americans was taken in 2014, use the normal
Given that P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.2, answer the following questions. a. What is P(Ac )? b. What is P(Bc )? c. What is P(A or B)? d. Are events A and B mutually
Suppose that three business executives drop their cell phones in an elevator and then pick them up at random. Describe how you could use index cards to conduct a simulation analysis to approximate

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