Questions and Answers of Introduction To Statistical Investigations

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
The 2012 U.S. Pet Ownership and Demographics Sourcebook reported that 36.5% of American households have a pet dog and 30.4% have a pet cat. a. Does it follow from this information that 36.5% +
According to the U.S. Census Bureau, the following table gives the probability distribution that a randomly chosen family household in the United States in 2016 has X members. A family household is
Given that P(A) = 0.80, P(B) = 0.50, and P(A and B) = 0.40, 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
Calvin is taking a 10-question true/false test and determining which answer to choose for each question by flipping a fair coin. He picks true if he gets heads and false if he gets tails. a.
If adult female guinea pigs weights are normally distributed with a mean of 800 grams and a standard deviation of 100 grams, using the empirical rule, what proportion of adult female guinea pigs
According to the Pew Research Center, in 2015, 58% of all American adults had Facebook accounts. Suppose this is true now. If a random sample of 100 Americans is to be taken, use the normal
Given that P(A) = 0.7, P(B)= 0.2, and P(A and B) = 0, 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 (call them Abby, Bernice, and Caitlin) drop their cell phones in an elevator and then pick them up at random. a. Write out the sample space of all possible
According to the U.S. Census Bureau, the following table gives the probability distribution that a randomly chosen nonfamily household in the United States in 2016 has Y members. A nonfamily
According to the Pew Research Center, in 2015, 58% of all American adults had Facebook accounts. Suppose this is true now. If a random sample of 100 Americans is to be taken, use the normal
Results from the Wechsler Adult Intelligence Scale, a common IQ test, are approximately normally distributed with a mean of 100 and a standard deviation of 15. a. Scores on the test that are 130
Suppose you toss three fair coins. a. What is the sample space? is one of the outcomes in the sample space and there are a total of 8 outcomes.) b. All 8 events you listed in part (a) are
Reconsider Exercise 11.1.8 about three business executives dropping their cell phones in an elevator and then picking them up at random. a. Report the probability that exactly one person picks
Suppose that there’s a 20% chance of rain on Saturday. The probabilities for Sunday depend on what happens on Saturday. If it rains on Saturday, then there’s an 80% chance of rain on Sunday and
Suppose you toss three fair coins as described in Exercise 11.3.9. (If you haven’t written out the sample space as described in Exercise 11.3.9, you should do that before answering the following
In Exercise 11.5.7 we looked at the probability distribution of the sum of two dice. This time we focus on using probability rules to derive the properties of the sum of two dice. a. Create a
Suppose that 28% of adults in a certain community have received a speeding ticket, that 42% have received a parking ticket, and that 17% have received both a speeding ticket and a parking ticket.
Suppose you toss three fair coins. a. What is the sample space? is one of the events in the sample space and there are a total of 8 events.) b. All eight events you listed in part (a) are
In 1941, Joe DiMaggio got at least one hit in 56 consecutive games, still the record for the longest hitting streak in Major League Baseball. Let’s try to estimate the probability of someone like
When two distributions are subtracted to form a new distribution, the new distribution must have a standard deviation of zero when which of A–E occur? (Choose all that apply.) A. The
Suppose that a couple has four children. Assume that all 16 outcomes in the sample space are equally likely. a. List the sample space of all possible outcomes for the sexes of these four
Suppose events A and B are independent, P(A) ≠ 0 and P(B) ≠ 0. Can events A and B also be mutually exclusive? Explain.
According to the Census Bureau, 33.4% of Americans 25 years old and older had a college degree (at least a bachelor’s) in 2016. a. If a random sample of 6 American 25 years old and older is
Which is NOT true about probability density functions? A. The total area under the curve of a probability density function and above the horizontal axis is 1. B. Using a probability density
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
Which of the following Venn diagrams correctly represents the situation where P(A) = 0.30, P(B) = 0.40, and P(A or B) = 0.60?A.B.C.D.E. 0.20 0.10 0.40 0.30 B
Suppose a fair coin is tossed 3 times and we let X represent the number of coins that land heads up. a. Create a probability distribution for X. b. What does the event X = 2 mean in this
Answer the following yes/no questions about simulation analyses. a. Is it possible to conduct a simulation analysis by hand, without using a computer? b. Are computers generally able to
One way that large families often decide who will give each other Christmas presents is to do a drawing. All the names go in a hat and each person draws a name and that is the person to whom he or
As estimated by the Pew Research Center in 2016, the probabilities associated with a randomly chosen American adult using Facebook and Twitter are shown in the following two-way table. a. What
In a game we will call “gambling dice,” you pay $1 to roll two dice. If you roll a sum of 5, 6, 7, or 8, you lose and don’t get your dollar back (you are out $1). If you roll anything else, you
About 51% of babies born in the United States are boys. Let’s assume that the probability of a birth resulting in a boy is 0.51 for all U.S. births. Suppose a couple decides they want to have four
Results from the Wechsler Adult Intelligence Scale, a common IQ test, are approximately normally distributed with a mean of 100 and a standard deviation of 15. a. There are various IQs for which
Use the Random Babies applet to investigate what happens as the number of babies (and mothers) increases. Start with only 2 babies, and then proceed to 4, 6, and 8 babies. For each number, simulate
Recall the probability distribution for family household size given in Exercise 11.4.8. a. What was the mean family household size in the United States in 2016? b. What was the standard
According to the Pew Research Center, in 2015, 19% of all American adults had Twitter accounts. Suppose this is true now. a. If a random sample of 500 Americans is taken, use the normal
An American roulette wheel has numbers 1 through 36, where the even numbers are black and odd numbers are red. There are also numbers 0 and 00, which are green. The wheel is spun and a ball will
As estimated by the Pew Research Center in 2016, the probabilities associated with a randomly chosen American adult using Facebook and Instagram are shown in the following two-way table. a. Use
Assuming the probability that a family has a boy or a girl is the same (0.50), if a family has three children, what is the probability that: a. The oldest two are girls and the youngest is a
As estimated by the Pew Research Center in 2016, the probabilities associated with a randomly chosen American adult using Facebook and Twitter are shown in the following two-way table. a. What
What are the mean and standard deviation for the two probability distributions for the number of boys and the number of girls in families of four from Exercise 11.6.10?Data from Exercise 11.6.10About

Showing 400 - 500 of 1041