Questions and Answers of Statistics Informed Decisions Using Data

The number of hits to a website follows a Poisson process. Hits occur at the rate of 3.0 per minute between 7:00 p.m. and 10:00 p.m. Given below are three scenarios for the number of hits to the
N = 230, n = 15, k = 200, x = 12 A hypergeometric probability experiment is conducted with the given parameters. Compute the probability of obtaining x successes.
N = 150, n = 10, k = 10, x = 1 A hypergeometric probability experiment is conducted with the given parameters. Compute the probability of obtaining x successes.
Suppose that a sample of peanut butter contains 0.3 insect fragments per gram. Compute the probability that the number of insect fragments in a 2-gram sample of peanut butter is each of the following
N = 150, n = 20, k = 30 Compute the mean and standard deviation of the hypergeometric random variable X.
N = 150, n = 10, k = 10 Compute the mean and standard deviation of the hypergeometric random variable X.
For the past 107 years, a certain state suffered 39 direct hits from major (category 3 to 5) hurricanes.Assume that this was typical and the number of hits per year follows a Poisson distribution.(a)
In Michigan’s Classic Lotto 47 Lottery, a player must choose six numbers between 1 and 47, inclusive. Six balls numbered from 1 to 47 are then randomly selected from an urn. The random variable X
In a neighborhood of 95 homes, 35 have pets.Suppose that 12 homes are selected at random. The random variable X represents the number of homes in the sample that have pets. What is the probability of
A manufacturer received an order of 250 computer chips. Unfortunately, 12 of the chips are defective.To test the shipment, the quality-control engineer randomly selects 20 chips from the box of 250
A baseball team has 25 players, seven of whom bat left-handed. Suppose that the manager of this team is frustrated with the way the team is playing, so he decides to randomly select nine players to
A hung jury is one that is unable to come to a unanimous decision regarding the guilt of the defendant. Suppose that there is a pool of 30 potential jurors, but 2 of the 30 potential jurors would
Suppose that you wake up for work in the dark and find that the lights do not work in your bedroom. In addition, your sock drawer is a mess and contains 12 black socks and 17 blue socks that
Suppose that a concrete manufacturer has made 200 concrete cylinders that are supposed to withstand 4000 pounds per square inch of pressure. As the quality-control manager, you decide to randomly
You are studying survival times for mice given a drug at one of three doses (Low, Medium, or High). You define two dummy variables:(a) With these definitions, write the expressions for the mean
The data in Table 8.25 were collected in order to study factors affecting the supply and demand for commercial air travel. Data on various aspects of commercial air travel for an arbitrarily chosen
It is beneficial to be able to estimate the yield of useful product of a tree based on measurements of the tree taken before it is harvested. Measurements on four such variables were taken on a
Data were collected to discern environmental factors affecting health standards. For 21 small regions we have data on the following variables: The data are given in Table 8.27. (a) Perform a
We have data on the distance covered by irrigation water in a furrow of a field. The data are to be used to relate the distance covered to the time since watering began. The data are given in Table
Twenty-five volunteer athletes participated in a study of cross-disciplinary athletic abilities. The group was comprised of athletes from football, baseball, water polo, volleyball, and soccer. None
In this problem we are trying to estimate the survival of liver transplant patients using information on the patients collected before the operation. The variables are: The data are given in Table
Thirty men and 30 women asthma sufferers are randomly assigned to one of three exercise programs. At the end of 1 month, the change in their blood oxygen saturation is measured (positive values are
Thirty participants aged 20 to 29 and 30 participants aged 40 to 49 are randomly assigned to one of five groups. Each group is given a list of words to recall. The lists vary in type from 1 = “most
Return to the information in Practice Exercise 2. The researchers decide to treat verb type as if it were a quantitative factor with values ranging from 1 to 5. They fit a regression model with
An avid backyard “birder” is comparing two different feeder designs to see which attracts more birds. She purchases three of each type of feeder and hangs each at randomly chosen locations. She
An avid backyard “birder” tests two different bird foods to see which attracts more birds. On six randomly selected days, she hangs two identical feeders side by side and fills them with two
You are studying treatments for anorexia. Patients are randomly assigned to one of four treatments: 1 = standard, 2 = group therapy, 3 = family therapy, 4 = cognitive behavioral therapy. Define the
A forest ecologist takes readings of soil moisture and organic content at one meter intervals sequentially along a transect (a straight line along the ground). If soil moisture is regressed on
A problem in a textbook states that the covariance matrix for x1 and x2 is The entry marked by ? is smudged, but you are certain it is either a 7 or a 9. Which must it be? 24 4 ?
A researcher studies the association between students’ rating of professors (good, fair, poor) and class size (small, large). If all the respondents come from the same handful of classes, what
To reduce the use of drugs and other harmful substances, some public schools have started to use dogs to locate undesirable substances. Many arguments have been directed against this practice,
Since regression methods require the errors to be normally distributed, you apply the χ2 goodness of fit test for normality to the residuals, and obtain a p value of 0.001. What does this suggest
A newspaper story gave the frequencies of armed robbery and auto theft for two neighboring communities. Do the data of Table 12.15 suggest different crime patterns of the communities? Table 12.15
An apartment owner believes that more of her poolside apartments are leased by single occupants than by those who share an apartment. The data in Table 12.16 were collected from current occupants. Do
In science experiments, a very small value of the χ2 statistic (one very near 0.0) is sometimes regarded with suspicion. Why?
A serious problem that occurs when conducting a sample survey by mail is that of delayed or no response. Late respondents delay the processing of data, while nonrespondents may bias results, unless a
Use the data on tree diameters given in Table 1.7 to test whether the underlying distribution is normal. Estimate the mean and variance from the data. Combine intervals to avoid small cell
Under what circumstances might the χ2 value be large but the contingency coefficient be low? How would you interpret that result?
Out of a class of 40 students, 32 passed the course. Of those that passed, 24 had taken the prerequisite course, while of those that failed, only 1 had taken the prerequisite. Test the hypothesis
To determine the gender balance of various job positions the personnel department of a large firm took a sample of employees from three job positions. The three job positions and the gender of
A machine has a record of producing 80% excellent, 18% good, and 2%unacceptable parts. After extensive repairs, a sample of 200 produced 157 excellent, 42 good, and 1 unacceptable part. Have the
The market research department for a large department store conducted a survey of credit card customers to determine whether they thought that buying with a credit card was quicker than paying cash.
In a clinical trial, patients with mild cases of COVID-19 are randomly assigned to either a placebo or a standard anti-malaria drug. The number of patients who develop heart arrhythmias are tabulated
Cochran and Chamlin (2006) used data from the National Opinion Research Council General Social Survey (NORC-GSS) to compare Whites’ and Backs’ opinions of the death penalty. The data consisted of
Prototype electric cars are randomly assigned to one of two charging regimens.Over the course of a three-month test period, engineers record the number of times the car was driven and the number of
It has been proposed that the size of the ventricle, a physiological feature of the brain as measured by X-rays, may be associated with abnormal EEG (brain wave)readings. Table 13.15 shows ventricle
Twelve adult males were put on a liquid diet in a weight-reducing plan. Weights were recorded before and after the diet. The data are shown in Table 14.10. Use the Wilcoxon signed rank test to
The test scores shown in Table 14.11 were recorded by two different professors for two sections of the same course. Using the Mann Whitney test and α = 0:05, determine whether the locations of the
Eight human molar teeth were sliced in half. For each tooth, one randomly chosen half was treated with a compound designed to slow loss of minerals; the other half served as a control. All tooth
Three teaching methods were tested on a group of 18 students with homogeneous backgrounds in statistics and comparable aptitudes. Each student was randomly assigned to a method and at the end of a
Hail damage to cotton, in pounds per planted acre, was recorded for four counties for three years. The data are shown in Table 14.14. Using years as blocks use the Friedman test to determine whether
A sociologist uses 10 independent variables (plus an intercept term) to predict “socioeconomic status.”(a) In a data set with n = 500, would R2 = 0.07 be “significant”?(b) Is the
The data in Table 8.24 represent the results of a test for the strength of an asphalt concrete mix. The test consisted of applying a compressive force on the top of different sample specimens. Two
Which of the following is a discrete probability distribution?Approach In a discrete probability distribution, the sum of the probabilities must equal 1, and all probabilities must be between 0 and
Graph the discrete probability distribution given in Table 1 from Example 2.Approach In the graph of a discrete probability distribution, the horizontal axis represents the values of the discrete
Compute the mean of the discrete random variable given in Table 1 from Example 2.Approach Find the mean of a discrete random variable by multiplying each value of the random variable by its
The basketball player from Example 2 is asked to shoot three free throws 100 times. Compute the mean number of free throws made.Approach The player shoots three free throws and the number made is
A term life insurance policy will pay a beneficiary a certain sum of money upon the death of the policyholder. These policies have premiums that must be paid annually. Suppose an 18- year-old male
Find the standard deviation of the discrete random variable given in Table 1 from Example 2.Approach We will use Formula (2a) with the unrounded mean μX = 2.39.Approach We will use Formula (2b)
Use statistical software or a graphing calculator to find the mean and the standard deviation of the random variable whose distribution is given in Table 1.Approach We will use a TI-84 Plus C
Suppose a life insurance company sells a $$210$,000 one-year term life insurance policy to a 25-year-old female for $$220$. The probability that the female survives the year is 0.999524. Compute
An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $$30$,000. If the economy grows at a moderate pace, the
In the game of roulette, a player can place an $$8$ bet on the number 13 and have a 1/38 probability of winning. If the metal ball lands on 13, the player gets to keep the $$8$ paid to play the
An experimental drug is administered to 60 randomly selected individuals, with the number of individuals responding favorably recorded.Determine which of the following probability experiments
A basketball player who makes 81% of his free throws is asked to shoot free throws until he misses. The number of free throws attempted is recorded.Determine which of the following probability
An investor randomly purchases 12 stocks listed on a stock exchange. Historically, the probability that a stock listed on this exchange will increase in value over the course of a year is 50%. The
n = 20, p = 0.01, x = 2 A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 5, p = 0.55, x = 3 A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 9, p = 0.4, x ≤ 3 A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 11, p = 0.15, x ≤ 4 A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 11, p = 0.75, x ≥ 8 A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
According to an airline, flights on a certain route are on time 75% of the time. Suppose 17 flights are randomly selected and the number of on-time flights is recorded.(a) Explain why this is a
A poll reported that 65% of adults were satisfied with the job the major airlines were doing.Suppose 9 adults are selected at random and the number who are satisfied is recorded.(a) Explain why this
According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and
Fourteen jurors are randomly selected from a population of 3 million residents. Of these 3 million residents, it is known that 40% are of a minority race. Of the 14 jurors selected, 2 are
According to an almanac, 70% of adult smokers started smoking before turning 18 years old.(a) Compute the mean and standard deviation of the random variable X, the number of smokers who started
Suppose that a recent poll found that 64% of adults believe that the overall state of moral values is poor.(a) Compute the mean and standard deviation of the random variable X, the number of adults
According to another almanac, 60% of adult smokers started smoking before turning 18 years old.(a) If 300 adult smokers are randomly selected, how many would we expect to have started smoking before
According to a survey, 21% of residents of a country 25 years old or older had earned at least a bachelor’s degree. You are performing a study and would like at least 10 people in the study to have
9!Find the value of each factorial.
13!Find the value of each factorial.
11!Find the value of each factorial.
3P2 Find the value of each permutation.
6P6 Find the value of each permutation.
4P2 Find the value of each permutation.
3P3 Find the value of each permutation.
8P1 Find the value of each permutation.
18P0 Find the value of each permutation.
6P3 Find the value of each permutation.
8P4 Find the value of each permutation.
5C4 Find the value of each combination.
11C5 Find the value of each combination.
11C8 Find the value of each combination.
10C8 Find the value of each combination.
7C1 Find the value of each combination.
1C1 Find the value of each combination.
41C2 Find the value of each combination.
46C5 Find the value of each combination.
List all the permutations of three objects x, y, and z taken two at a time without repetition. What is 3P2?
List all the permutations of four objects w, x, y, and z taken two at a time without repetition. What is 4P2?

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