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statistics informed decisions using data

Statistics Informed Decisions Using Data 5th Global Edition Michael Sullivan - Solutions

On ten days, a bank had 18, 15, 13, 12, 8, 3, 7, 14, 16, and 3 bad checks. Find the mean, median, variance, and standard deviation of the number of bad checks.
Calculate the mean and standard deviation of the following sample: -1, 4, 5, 0.
The following is the distribution of ages of students in a graduate course:(a) Construct a bar chart of the data.(b) Calculate the mean and standard deviation of the data. Age (years) Frequency 20-24 11 25-29 24 30-34 30 35-39 18 40-44 11 45-49 50-54 51 5
The percentage change in the consumer price index (CPI) is widely used as a gauge of inflation. The following numbers show the percentage change in the average CPI for the years 1993 through 2007:(a) Using time as the horizontal axis and CPI as the vertical axis, construct a trend graph showing how
Most of the problems in this and other chapters deal with “real” data for which computations are most efficiently performed with computers. Since a little experience in manual computing is healthy, here are 15 observations of a variable having no particular meaning:(a) Compute the mean, median,
Because waterfowl are an important economic resource, wildlife scientists study how waterfowl abundance is related to various environmental variables. In such a study, the variables shown in Table 1.15 were observed for a sample of 52 ponds.WATER: the amount of open water in the pond, in acres.VEG:
Someone wants to know whether the direction of price movements of the general stock market, as measured by the New York Stock Exchange (NYSE)Composite Index, can be predicted by directional price movements of the New York Futures Contract for the next month. Data on these variables have been
The data in Table 1.17 consist of 25 values for four computer-generated variables called Y1, Y2, Y3, and Y4. Each of these is intended to represent a particular distributional shape. Use a stem and leaf and a box plot to ascertain the nature of each distribution and then see whether the empirical
Climatological records provide a rich source of data suitable for description by statistical methods. The data for this example (Table 1.18) are the number of January days in London, England, having rain (Days) and the average January temperature (Temp, in degrees Fahrenheit) for the years 1858
Make scatterplots for all pairwise combinations of the variables from the tree data(Table 1.7). Which pairs of variables have the strongest relationship? Is your conclusion consistent with prior knowledge? Table 1.7 Data on tree measurements. OBS DFOOT HCRN HT OBS DFOOT HCRN HT OBS DFOOT HCRN HT
The data in Table 1.20 show statistics on the age distribution of Chinese victims of COVID-19. (These data, from China CDC Weekly, are dated February 11, 2020, when the pandemic was well underway in China.)(a) Produce relative frequency histograms for the ages of the cases and deaths.To handle the
The use of placement exams in elementary statistics courses has been a controversial topic in recent times. Some researchers think that the use of a placement exam can help determine whether a student will successfully complete a course (or program). A recent study in a large university resulted in
_______________If two events are mutually exclusive, then P(A or B) = P(A) + P(B).
_______If A and B are two events, then P(A and B) = P(A)P(B), no matter what the relation between A and B.
This section consists of some true/false questions regarding concepts of statistical inference. Indicate if a statement is true or false and, if false, indicate what is required to make the statement true. __________ The probability distribution function of a discrete random variable cannot have a
________ The probability density function of a continuous random variable. can take on any value, even negative ones.
This section consists of some true/false questions regarding concepts of statistical inference. Indicate if a statement is true or false and, if false, indicate what is required to make the statement true. __________ The probability that a continuous random variable lies in the interval 4 to 7,
_______ A normal distribution is characterized by its mean and its degrees of freedom.
This section consists of some true/false questions regarding concepts of statistical inference. Indicate if a statement is true or false and, if false, indicate what is required to make the statement true. __________ The standard normal distribution has mean zero and variance σ2.
__________ The t distribution is used as the sampling distribution of the mean if the sample is small and the population variance is known.
__________ The standard error of the mean increases as the sample size increases.
__________ As α increases, the value of zα will decrease.
The weather forecast says there is a 40% chance of rain today and a 30% chance of rain tomorrow. Assume the days are independent.(a) What is the chance of rain on both days?(b) What is the chance of rain on neither day?(c) What is the chance of rain on at least one day?
The following is a probability distribution of the number of defects on a given contact lens produced in one shift on a production line: Let A be the event that one defect occurred, and B be the event that 2, 3, or 4 defects occurred. Find:(a) P(A) and P(B)(b) P(A and B)(c) P(A or B) Number of
Suppose that Y is a normally distributed random variable with μ = 10 and σ = 2, and X is an independent random variable, also normally distributed with μ = 5 and σ = 5. Find: (a) P(Y>12 and X>4) (b) P(Y 12 or X>4) (c) P(Y10 and X
In a sample of size 5 from a normal distribution, which is more likely: that the sample variance will be less than half the true variance, or that it will be more than twice the true variance?
Suppose Y = home price per square foot has a normal distribution with a mean of 100 and a standard deviation of 20.(a) What value separates the most expensive 25% of homes from the less expensive 75%?(b) What values separate the middle 50% of the homes from the rest?
A randomly selected home has a 32% chance of having a fireplace. If you randomly select records for 12 homes, what is the probability that:(a) exactly 4 have a fireplace?(b) at least 7 have a fireplace?
A lottery that sells 150,000 tickets has the following prize structure: (1) first prize of \($50,000\)(2) 5 second prizes of \($10,000\)(3) 25 third prizes of \($1000\)(4) 1000 fourth prizes of \($10\)(a) Let Y be the winning amount of a randomly drawn lottery ticket. Describe the probability
Assume the random variable y has the continuous uniform distribution defined on the interval a to b, that is, For this problem let a = 0 and b = 2. (a) Find P(Y (b) Find μ and σ2 for the distribution. == f(y) 1/(ba), a y b.
The binomial distribution for p = 0:2 and n = 5 is:(a) Compute μ and σ2 for this distribution.(b) Do these values agree with those obtained as a function of the parameter p and sample size n? Value of Y Probability 0 1 2 3 4 5 0.3277 0.4096 0.2048 0.0512 0.0064 0.0003
A system requires two components, A and B, to both work before the system will. Because of the sensitivity of the system, an increased reliability is needed. To obtain this reliability, two duplicate components are to be used. That is, the system will have components A1;A2; B1; and B2. An engineer
Let Y be a normally distributed random variable with mean 10 and variance 25. Find: (a) P(Y>15) (b) P(8
A teacher finds that the scores of a particularly difficult test were approximately normally distributed with a mean of 76 and standard deviation of 14.(a) If a score below 60 represents a grade of F (failure), approximately what percent of students failed the test?(b) If the cutoff for a grade
A random sample of 100 is taken from a population with a mean of 140 and standard deviation of 25. What is the probability that the sample mean lies between 138 and 142?
A manufacturer wants to state a specific guarantee for the life of a product with a replacement for failed products. The distribution of lifetimes of the product is normal and has a mean of 1000 days and standard deviation of 150 days. What life length should be stated in the guarantee so that only
A teacher wants to curve her grades such that 10% are below 60 and 10% above 90. Assuming a normal distribution, what values of μ and σ2 will provide such a curve?
Historically, victims of the Ebola virus had a 30% chance of survival.(a) A new treatment is tested on three victims, and at least two of them survive. What is the probability of this happening, if the treatment is not effective?(b) The new treatment is tested on six victims, and at least four of
Suppose the sales price per square foot of homes follows an approximate normal distribution. If you construct a box plot based on a large dataset for this variable, about what percentage of the sample will be labeled as outliers?
To monitor the production of sheet metal screws by a machine in a large manufacturing company, a sample of 100 screws is examined each hour for three shifts of 8 hours each. Each screw is inspected and designated as conforming or nonconforming according to specifications. Management is willing to
Based on data from the 2007 National Health Interview Survey, it is estimated that “10% of adults experienced feelings of sadness for all, most, or some of the time” during the 30 days prior to the interview. You interview a random sample of 68 people who have recently filed for unemployment
The Kaufman Assessment Battery for Children is designed to measure achievement and intelligence with a special emphasis on nonverbal intelligence. Its global measures, such as its Sequential Processing score, are scaled to have a mean of 100 and a standard deviation of 15. Assume that the
The number of birth defects in a region is commonly modeled as having a binomial distribution, with a rate of three birth defects per 100 births considered a typical rate in the United States.(a) What is the probability a county that had 50 independent births during the year would have more than
Twelve patients undergoing recuperation from cardiothoracic surgery are randomly divided into two groups. Because the treatment that one group is about to receive affects blood glucose levels, the researchers first compare values of A1C (a measure of blood glucose control over the last 120 days) in
______ If the test statistic falls in the rejection region, the null hypothesis has been proven to be true.
______ The risk of a type II error is directly controlled in a hypothesis test by establishing a specific significance level.
______ If the null hypothesis is true, increasing only the sample size will increase the probability of rejecting the null hypothesis.
______ If the null hypothesis is false, increasing the level of significance (α) for a specified sample size will increase the probability of rejecting the null hypothesis.
______ If we decrease the confidence coefficient for a fixed n, we decrease the width of the confidence interval.
______ If a 95% confidence interval on μ was from 50.5 to 60.6, we would reject the null hypothesis that μ = 60 at the 0.05 level of significance.
______ If the sample size is increased and the level of confidence is decreased, the width of the confidence interval will increase.
This section consists of some true/false questions regarding concepts of statistical inference. Indicate whether a statement is true or false and, if false, indicate what is required to make the statement true. ______ A research article reports that a 95% confidence interval for mean reaction
The following sample was taken from a normally distributed population with a known standard deviation σ = 4. Test the hypothesis that the mean μ = 20 using a level of significance of 0.05 and the alternative that μ > 20: 23, 32, 22, 31, 27, 25, 21, 24, 20, 18.
A note on your results states “z = 1:87:” Calculate the p value assuming: (a) H: >Ho (b) H: (b) H:
In testing the null hypothesis that p = 0:3 against the alternative that p ≠ 0:3, the probability of a type II error is ______ when the true p = 0:4 than when p = 0:6. (1) the same (2) smaller (3) larger (4) none of the above
In a hypothesis test the p value is 0.043. This means that we can find statistical significance at: (1) both the 0.05 and 0.01 levels (2) the 0.05 but not at the 0.01 level (3) the 0.01 but not at the 0.05 level (4) neither the 0.05 or 0.01 levels (5) none of the above
An article states “there is no significant evidence that median income increased.” The implied null hypothesis is: (1) Median income increased. (2) Median income changed. (3) Median income did not increase. (4) Median income decreased. (5) There is insufficient information to decide.
A probability experiment consists of rolling a single fair die.(a) Identify the outcomes of the probability experiment.(b) Determine the sample space.(c) Define the event E = “roll an even number.”Approach The outcomes are the possible results of the experiment. The sample space is a list of
The data in Table 2 represent the results of a survey in which 200 people were asked their means of travel to work.(a) Use the survey data to build a probability model for means of travel to work.(b) Estimate the probability that a randomly selected individual carpools to work. Interpret this
A pair of fair dice is rolled. Fair die are die where each outcome is equally likely.(a) Compute the probability of rolling a seven.(b) Compute the probability of rolling “snake eyes”; that is, compute the probability of rolling a two.(c) Comment on the likelihood of rolling a seven versus
Sophia has three tickets to a concert, but Yolanda, Michael, Kevin, and Marissa all want to go to the concert with her. To be fair, Sophia randomly selects the two people who can go with her.(a) Determine the sample space of the experiment. In other words, list all possible simple random samples of
Suppose that a survey asked 500 families with three children to disclose the gender of their children and found that 180 of the families had two boys and one girl.(a) Estimate the probability of having two boys and one girl in a three-child family using the empirical method.(b) Compute and
(a) Simulate the experiment of sampling 100 three-child families to estimate the probability that a three-child family has two boys.(b) Simulate the experiment of sampling 1000 three-child families to estimate the probability that a three-child family has two boys.Approach To simulate
Our number system consists of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Because we do not write numbers such as 12 as 012, the first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. We may think that each digit appears with equal frequency so that each digit has a 1/9
Suppose that a single card is selected from a standard 52-card deck, such as the one shown in Figure 9.(a) Compute the probability of the event E = “drawing a king.”(b) Compute the probability of the event E = “drawing a king” or F = “drawing a queen” or G = “drawing a
Suppose a single card is selected from a standard 52-card deck. Compute the probability of the event E = “drawing a king” or F = “drawing a diamond.”Approach The events are not disjoint because the outcome “king of diamonds” is in both events, so use the General Addition Rule.
Using the data in Table 6,(a) Determine the probability that a randomly selected U.S. resident 15 years old or older is male.(b) Determine the probability that a randomly selected U.S. resident 15 years old or older is widowed.(c) Determine the probability that a randomly selected U.S. resident 15
According to the National Gambling Impact Study Commission, 52% of Americans have played state lotteries. What is the probability that a randomly selected American has not played a state lottery?Approach Not playing a state lottery is the complement of playing a state lottery. Compute the
The data in Table 7 represent the income distribution of households in the United States in 2013.Compute the probability that a randomly selected household earned the following incomes in 2013:(a) $200,000 or more (b) Less than $200,000 (c) At least $10,000 Table 7 Annual Income Number Annual
If P(E) = 0.55, P(E or F) = 0.70, and P(E and F) = 0.15, find P(F).
If P(F) = 0.30, P(E or F) = 0.65, and P(E and F) = 0.15, find P(E).
The following data represent the number of live multiple-delivery births (three or more babies) in a particular year for women 15 to 54 years old.(a) Determine the probability that a randomly selected multiple birth for women 15–54 years old involved a mother 30 to 39 years old.(b) Determine the
Birthdays Exclude leap years from the following calculations:(a) Compute the probability that a randomly selected person does not have a birthday on December 6.(b) Compute the probability that a randomly selected person does not have a birthday on the 4th day of a month.(c) Compute the probability
According to a study, the probability that a randomly selected person has hearing problems is 0.149. The probability that a randomly selected person has vision problems is 0.085. Can we compute the probability of randomly selecting a person who has hearing problems or vision problems by adding
According to a survey, the probability that a randomly selected worker primarily rides a bicycle to work is 0.792. The probability that a randomly selected worker primarily takes public transportation to work is 0.071.(a) What is the probability that a randomly selected worker primarily rides a
Cigar Smoking The data in the following table show the association between cigar smoking and death from cancer for 139,704 men. Note: Current cigar smoker means cigar smoker at time of death.(a) If an individual is randomly selected from this study, what is the probability that he died of
A university conducted a survey of 366 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank.(a) If a survey participant is selected at random, what is the probability that he or she is satisfied with student government?(b)
Driver Fatalities The data in the table represent the number of drivers involved in fatal crashes in a certain region by day of the week and gender.(a) Determine the probability that a randomly selected fatal crash involved a female.(b) Determine the probability that a randomly selected fatal crash
Go to the book’s website to obtain the data file SullivanStatsSurveyI using the file format of your choice for the version of the text you are using. The data represent the results of a survey conducted by the author. The variable “Text while Driving” represents the response to the question,
In the game of roulette, the wheel has slots numbered 0, 00, and 1 through 36.A metal ball rolls around a wheel until it falls into one of the numbered slots. What is the probability that the ball will land in the slot numbered 17 two times in a row?Approach The sample space of the experiment has
The probability that a randomly selected 24-year-old male will survive the year is 0.9986 according to the National Vital Statistics Report, Vol. 56, No. 9.(a) What is the probability that three randomly selected 24-year-old males will survive the year?(b) What is the probability that 20 randomly
Compute the probability that at least one male out of 1000 aged 24 years will die during the course of the year if the probability that a randomly selected 24- year old male survives the year is 0.9986.Approach The phrase at least means “greater than or equal to,” so we wish to know the
Suppose that E and F are two events and that N(E and F) = 210 and N(E) = 330. What is P(F|E)?
Suppose events E and F are disjoint. What is P(E and F )?
Determine whether the events E and F are independent or dependent. Justify your answer.(a) E: A person living at least 70 years.F: The same person regularly handling venomous snakes.(b) E: A randomly selected person accidentally killing a spider.F: Another randomly selected person accidentally
Suppose that events E and F are independent, P(E) = 0.3 and P(F) = 0.8. What is P(E and F)?
Suppose that events E and F are independent, P(E) = 0.4 and P(F) = 0.8. What is P(E and F)?
What is the probability of obtaining eleven tails in a row when flipping a coin? Interpret this probability.
About 5% of the population of a large country is math-phobic. If two people are randomly selected, what is the probability both are math-phobic? What is the probability at least one is math-phobic?
A test to determine whether a certain antibody is present is 99.7% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject). The probability of a test coming back positive when the antibody is not present (a false positive) is
The probability that a randomly selected 1-year-old male chipmunk will live to be 2 years old is 0.97853.(a) What is the probability that two randomly selected 1-yearold male chipmunks will live to be 2 years old?(b) What is the probability that five randomly selected 1-yearold male chipmunks will
A grocery bag can be classified as either paper or plastic. 96% of grocery bags are classified as plastic.(a) Two grocery bags are chosen at random. What is the probability that both grocery bags are plastic?(b) Five grocery bags are chosen at random. What is the probability that all five grocery
Suppose Nate loses 41% of all thumb wars.(a) What is the probability that Nate loses two thumb wars in a row?(b) What is the probability that Nate loses six thumb wars in a row?(c) When events are independent, their complements are independent as well. Use this result to determine the probability
Among 52- to 57-year-olds, 29% say they have danced in public while under the influence of alcohol.Suppose five 52- to 57-year-olds are selected at random.(a) What is the probability that all five have danced in public while under the influence of alcohol?(b) What is the probability that at least
For the fiscal year 2007, a tax authority audited 1.65% of individual tax returns with an income of \($100\),000 or more. Suppose this percentage stays the same for the current tax year. What is the probability that two randomly selected returns with an income of \($100\),000 or more will be
Suppose a single die is rolled. What is the probability that the die comes up three? Now suppose that the die is rolled a second time, but we are told the outcome will be an odd number. What is the probability that the die comes up three?Approach Assume that the die is fair. This means that the
The data in Table 8 on the previous page represent the marital status and gender of the residents of the United States aged 15 years old or older in 2013.(a) Compute the probability that a randomly selected individual has never married given the individual is male.(b) Compute the probability that a
Suppose that 12.7% of all births are preterm. (The gestation period of the pregnancy is less than 37 weeks.) Also 0.22% of all births resulted in a preterm baby who weighed 8 pounds, 13 ounces or more. What is the probability that a randomly selected baby weighs 8 pounds, 13 ounces or more, given
The probability that a driver who is speeding gets pulled over is 0.8. The probability that a driver gets a ticket, given that he or she is pulled over, is 0.9. What is the probability that a randomly selected driver who is speeding gets pulled over and gets a ticket?Approach Let E represent the
Suppose that of 100 circuits sent to a manufacturing plant, 5 are defective. The plant manager receiving the circuits randomly selects 2 and tests them. If both circuits work, she will accept the shipment. Otherwise, the shipment is rejected. What is the probability that the plant manager discovers

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