Questions and Answers of Statistics Informed Decisions Using Data

A woman has eight skirts and four blouses. Assuming that they all match, how many different skirt and- blouse combinations can she wear?
A woman has ten skirts and five blouses. Assuming that they all match, how many different skirt-and blouse combinations can she wear?
Suppose Aaron is going to burn a compact disk (CD) that will contain 11 songs. In how many ways can Aaron arrange the 11 songs on the CD?
A salesperson must travel to five cities to promote a new marketing campaign. How many different trips are possible if any route between cities is possible?
Randomly Playing Songs A certain digital music player randomly plays each of 10 songs. Once a song is played, it is not repeated until all the songs have been played. In how many different ways can
In the game show Deal or No Deal?, a contestant is presented with 26 suitcases that contain amounts ranging from $0.01 to $1,000,000. The contestant must pick an initial case that is set aside as the
According to a Harris poll, 14% of adult Americans have one or more tattoos, 50% have pierced ears, and 65% of those with one or more tattoos also have pierced ears. What is the probability that a
The Hazelwood city council consists of five men and four women. How many different subcommittees can be formed that consist of three men and two women?Approach Follow the flowchart in Figure 17.
The Daytona 500, the season opening NASCAR event, has 43 drivers in the race. In how many different ways could the top four finishers (first, second, third, and fourth place) occur?Approach Follow
E = {6, 10}.Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose that the outcomes are equally likely. Compute the probability of the event:
E = “an odd number.”Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose that the outcomes are equally likely. Compute the probability of the event:
6!2!/4!Evaluate each expression.
5P3 Evaluate each expression.
E = {red or blue or yellow} Let the sample space be S = {red, green, blue, orange, yellow}. Suppose that the outcomes are equally likely. Compute the probability of the event:
Suppose that P(E) = 0.76, P(F) = 0.45, and P(E and F) = 0.32. What is P(E or F)?
Suppose that there are two urns. Urn I contains four black and three white balls. Urn II contains four black, seven white, and two red balls. Suppose that we roll a fair die. If the die is a one or a
Redo Example 1 using Formula (1). Approach We will define the events as we did in Example 1. We want the probability of selecting a black ball. This can occur by selecting urn I and then selecting
Suppose that a calculator manufacturer buys integrated circuits from three different suppliers: supplier I, supplier II, and supplier III. Based on past experience, it is known that 2% of circuits
According to the U.S. Census Bureau, 27.3% of U.S. adult women have never married (single), 49.8% of U.S. adult women are married, and 22.8% of U.S. adult women are widowed, divorced, or separated
Refer to Examples 1 and 2. Suppose that a black ball was selected. What is the probability that the black ball came from urn I?Approach We know that P(U) = 1 P(U) = 3 4 P(B|U) = P(B|U2) 23 4 = P(B) =
According to the U.S. Census Bureau, 27.3% of U.S. adult women have never married (single), 49.8% of U.S. adult women are married, and 22.8% of U.S. adult women are widowed, divorced, or separated
Persons are classified as work disabled if they have a health problem that prevents them from working in the type of work they can do. Table 12 on the next page contains the proportion, by age, of
Suppose that S is a sample space. What would it mean to partition S into three disjoint subsets A1, A2, and A3? Draw a figure to help support your explanation.
What must be true regarding the sum of the probability of events that make up the partitions of the sample space?
Describe the Rule of Total Probability in your own words.
What is the difference between a priori and a posteriori probabilities? Which is Bayes’s Rule used for?
P(E|A)Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3 P(C)
P(E|B)Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3 P(C)
P(Ec|A) Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3
P(Ec|B)Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3 P(C)
P(E|C)Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3 P(C)
P(Ec|C) Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3
P(E)Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3 P(C) =
P(Ec) Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3 P(C)
P(A|E)Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3 P(C)
P(A|Ec)Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3 P(C)
P(C|E) Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3
P(B|Ec)Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3 P(C)
P(B|E)Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3 P(C)
P(C|Ec)Find the indicated probabilities by referring to the given tree diagram and by using Bayes’s Rule. A P(A) = 0.2 P(E|A)=0.6 E P(ECA) = 0.4 -EC P(B) = 0.55 P(E|B)=0.7 -E B EC P(E|B) = 0.3 P(C)
Suppose that events A1 and A2 form a partition of the sample space S with P(A1) = 0.55 and P(A2) = 0.45. If E is an event that is a subset of S and P(E|A1) = 0.06 and P(E|A2) = 0.08, find P(E).
Suppose that events A1 and A2 form a partition of the sample space S with P(A1) = 0.35 and P(A2) = 0.65. If E is an event that is a subset of S and P(E|A1) = 0.12 and P(E|A2) = 0.09, find P(E).
Suppose that events A1, A2, and A3 form a partition of the sample space S with P(A1) = 0.35, P(A2) = 0.45, and P(A3) = 0.2. If E is an event that is a subset of S and P(E|A1) = 0.25, P(E|A2) = 0.18,
Suppose that events A1, A2, and A3 form a partition of the sample space S with P(A1) = 0.3, P(A2) = 0.65, and P(A3) = 0.05. If E is an event that is a subset of S and P(E|A1) = 0.05,P(E|A2) = 0.25,
Use the information given in Problem 21 to find:(a) P(A1|E)(b) P(A2|E)Data from Problem 21Suppose that events A1 and A2 form a partition of the sample space S with P(A1) = 0.55 and P(A2) = 0.45. If E
Use the information given in Problem 22 to find:(a) P(A1|E)(b) P(A2|E)Data from Problem 22Suppose that events A1 and A2 form a partition of the sample space S with P(A1) = 0.35 and P(A2) = 0.65. If E
Use the information given in Problem 23 to find:(a) P(A1|E)(b) P(A2|E)(c) P(A3|E)Data from Problem 23Suppose that events A1, A2, and A3 form a partition of the sample space S with P(A1) = 0.35, P(A2)
Use the information given in Problem 24 to find:(a) P(A1|E)(b) P(A2|E)(c) P(A3|E)Data from Problem 24Suppose that events A1, A2, and A3 form a partition of the sample space S with P(A1) = 0.3, P(A2)
Urn I contains five black and seven white balls. Urn II contains six black, five white, and three red balls. Roll a fair die.If the die is a one, three, or five, randomly select a ball from urn I.
Urn I contains eleven black and nine white balls and urn II contains three black, eight white, and six red balls. Roll a fair die.If the die is a one, three, or five, randomly select a ball from urn
Urn I contains six black and nine white balls; urn II contains five black, twelve white, and nine red balls; and urn III contains eleven black, six white, and twelve red balls. Roll a fair die. If
Urn I contains seven black and three white balls; urn II contains twelve black, five white, and six red balls; and urn III contains one black, eight white, and four red balls. Roll a fair die.If the
Color Blindness The most common form of color blindness is red–green color blindness. People with this type of color blindness cannot distinguish between green and red.Approximately 8% of all males
ELISA Test The standard test for the HIV virus is the ELISA test, which tests for the presence of HIV antibodies. If an individual does not have the HIV virus, the test will come back negative for
The data in the following table represent the proportion of Americans 25 years of age or older at various levels of educational attainment in 2013.If we let M represent the event that a randomly
Refer to Problem 35. If we let E represent the event that a randomly selected American who is 25 years of age or older is employed, we can also obtain the following probabilities from the Census
Voting Pattern The following data represent the proportion of Americans who voted in the 2012 presidential election at various levels of educational attainment.If we let D represent the event that a
The following data represent the proportion of murder victims at various age levels in 2013.If we let M represent the event that a randomly selected murder victim was male, we can also obtain the
The CIA suspects that one of its operatives is a double agent. Past experience indicates that 95% of all operatives suspected of espionage are, in fact, guilty. The CIA decides to administer a
If we decrease the confidence level, the width of the confidence interval will: (1) increase (2) remain unchanged (3) decrease (4) double (5) none of the above
_______ The t distribution is more dispersed than the normal.
Indicate true or false for the following statements. If false, specify what change will make the statement true. _______ The χ2 distribution is used for inferences on the mean when the variance is
_______ The mean of the t distribution is affected by the degrees of freedom.
_______ The quantity has the t distribution with (n - 1) degrees of freedom. (H) 2/n
_______ In the t test for a mean, the level of significance increases if the population standard deviation increases, holding the sample size constant.
Indicate true or false for the following statements. If false, specify what change will make the statement true. _______ The χ2 distribution is used for inferences on the variance.
_______ The mean of the t distribution is zero.
Indicate true or false for the following statements. If false, specify what change will make the statement true. _______ When the test statistic is t and the number of degrees of freedom is >30,
Indicate true or false for the following statements. If false, specify what change will make the statement true. _______ The χ2 distribution is skewed and its mean is always 2.
Indicate true or false for the following statements. If false, specify what change will make the statement true. _______ The sampling distribution of a proportion is approximated by the χ2
_______ The t test can be applied with absolutely no assumptions about the distribution of the population.
A manufacturer of watches has established that on the average his watches do not gain or lose. He also would like to claim that at least 95% of the watches are accurate to ±0.2 s per week. A random
A sample of 20 insurance claims for automobile accidents (in $$1000$) gives the following values: Construct a 0.95 confidence interval on the mean value of claims. Comment on the usefulness of
It is said that the average weight of healthy 12-hour-old infants is supposed to be 7.5 lb. A sample of newborn babies from a low-income neighborhood yielded the following weights (in pounds) at 12
A production line in a certain factory puts out washers with an average inside diameter of 0.10 in. A quality control procedure that requires the line to be shut down and adjusted when the standard
This experiment concerns the precision of one type of collecting tubes used for air sampling of hydrofluoric acid. The tubes are tested three times at five different concentrations. The data shown in
_______________________ One of the assumptions underlying the use of the (pooled) two-sample test is that the samples are drawn from populations having equal means.
_______________________ In the two-sample t test, the number of degrees of freedom for the test statistic increases as sample sizes increase.
_______________________ A two-sample test is twice as powerful as a one sample test.
Indicate true or false for the following statements. If false, specify what change will make the statement true. _______________________ If every observation is multiplied by 2, then the t statistic
_______________________ When the means of two independent samples are used to compare two population means, we are dealing with dependent (paired) samples.
_______________________ The use of paired samples allows for the control of variation because each pair is subject to the same common sources of variability.
Indicate true or false for the following statements. If false, specify what change will make the statement true. _______________________ The χ2 distribution is used for making inferences about two
_______________________ The F distribution is used for testing differences between means of paired samples.
_______________________ The standard normal (z) score may be used for inferences concerning population proportions.
Indicate true or false for the following statements. If false, specify what change will make the statement true. _______________________ The F distribution is symmetric and has a mean of 0.
Indicate true or false for the following statements. If false, specify what change will make the statement true. _______________________ The F distribution is skewed and its mean is close to 1.
_______________________ The pooled variance estimate is used when comparing means of two populations using independent samples.
_______________________ It is not necessary to have equal sample sizes for the paired t test.
_______________________ If the calculated value of the t statistic is negative, then there is strong evidence that the null hypothesis is false.
Two sections of a class in statistics were taught by two different methods. Students’ scores on a standardized test are shown in Table 5.13. Do the results present evidence of a difference in the
To assess the effectiveness of a new diet formulation, a sample of 8 steers is fed a regular diet and another sample of 10 steers is fed a new diet. The weights of the steers at 1 year are given in
In a test of the effectiveness of a device that is supposed to increase gasoline mileage in automobiles, 12 cars were run, in random order, over a prescribed course both with and without the device
A new method of teaching children to read promises more consistent improvement in reading ability across students. The new method is implemented in one randomly chosen class, while another class is
A company offers a seminar on a technical subject to its employees. Before the seminar begins, each employee scores their self-rating of knowledge on the subject. Three months after the seminar, each
Chlorinated hydrocarbons (mg/kg) found in samples of two species of fish in a lake are as follows: Perform a hypothesis test to determine whether there is a difference in the mean level of
A large hospital administers a “compassion burnout” survey to a random sample of nurses. The responses are scored on a scale of 0 = least burnout to 20 = most burnout. The responses of the nurses
Eight samples of effluent from a pulp mill were each divided into 10 batches. From each sample, 5 randomly selected batches were subjected to a treatment process intended to remove toxic substances.
Elevated levels of blood urea nitrogen (BUN) denote poor kidney function. Ten elderly cats showing early signs of renal failure are randomly divided into two groups. Group 1 (control group) is placed
In the 2020 Covid-19 pandemic, a number of emergency observational studies were carried out to evaluate hydro chloroquine (HCQ) as a potential treatment. Table 5.23 reports the results of a French

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