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mathematics
statistics

Questions and Answers of Statistics

It is believed that at least 60% of the residents in a certain area favor an annexation suit by a neighboring city. What conclusion would you draw if only 110 in a sample of 200 voters favor the
A fuel oil company claims that one-fifth of the homes in a certain city are heated by oil. Do we have reason to believe that fewer than 1/5 are heated by oil if, in a random sample of 1000 homes in
At a certain college it is estimated that at most 25% of the students ride bicycles to class. Does this seem to be a valid estimate if, in a random sample of 90 college students, 28 are found to ride
A new radar device is being considered for a certain defense missile system. The system is checked by experimenting with actual aircraft in which a kill or a no kill is simulated. If in 300 trials,
In a controlled laboratory experiment, scientists at the University of Minnesota discovered that 25% of a certain strain of rats subjected to a 20% coffee bean diet and then force-fed a powerful
In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 63 of 100 urban residents favor the
In a study on the fertility of married women conducted by Martin O'Connell and Carolyn C. Rogers for the Census Bureau in 1979, two groups of childless wives aged 25 to 29 were selected at random and
An urban community would like to show that the incidence of breast cancer is higher than in a nearby rural area. (PCB levels were found to be higher in the soil of the urban community.) If it is
In a winter of an epidemic flu, 2000 babies were surveyed by a well-known pharmaceutical company to determine if the company's new medicine was effective after two days. Among 120 babies who had the
The volume of containers of a particular lubricant is known to be normally distributed with a variance of 0.03 liter, Test the hypothesis that σ2 = 0.03 against the alternative that a2 ≠ 0.03 for
Past experience indicates that the time required for high school seniors to complete a standardized test is a normal random variable with a standard deviation of 6 minutes. Test, the hypothesis that
All toxins produced by mold on peanut crops in Virginia must be monitored. A sample of 61 batches of peanuts reveals levels of 24.17 ppm, on average, with a variance of 4.25 ppm. Test the hypothesis
Past data indicate that, the amount of money contributed by the working residents of a large city to a volunteer rescue squad is a normal random variable with a standard deviation of S1.40. It has
A soft-drink dispensing machine is said to be out of control if the variance of the contents exceeds 1.15 deciliters. If a random sample of 25 drinks from this machine has a variance of 2.03
Large-Sample Test of a2 = ?02: When n > 30 we can test the null hypothesis that ? = ?02, or ? ? (To, by computing which is a value of a random variable whose sampling distribution is approximately
A study is conducted to compare the length of time between men and women to assemble a certain product. Past experience indicates that the distribution of times for both men and women is
In Exercise 10.41, test the hypothesis at the 0.05 level of significance that σ21 = σ22 against the alternative that, σ21 ≠ σ22, where σ21 and σ22 are the variances for the number of
With reference: to Exercise 10.39, test the hypothesis that a\ = σ22 against the alternative that a\ = σ22, where σ21 and σ22 are the variances for the running times of films produced by company
Two types of instruments for measuring the amount of sulfur monoxide in the atmosphere are being compared in an air-pollution experiment. It is desired to determine whether the two types of
A soft-drink dispensing machine is said to be out of control if the variance of the contents exceeds 1.15 deciliters. If a random sample of 25 drinks from this machine has a variance of 2.03
A soft-drink dispensing machine is said to be out of control if the variance of the contents exceeds 1.15 deciliters. If a random sample of 25 drinks from this machine has a variance of 2.03
A die is tossed 180 times with the following results. Is this a halanced die? Use a 0.01 level ofsignificance.
In 100 tosses of a coin, 63 heads and 37 tails are ohserved. Is this a balanced coin? Use a 0.05 level of significance.
A machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1. A can containing 500 of these mixed nuts was found to have 269 peanuts, 112 hazelnuts, 74 cashews, and 45
The grades in a statistics course for a particular semester were as follows. Test the hypothesis, at the 0.05 level of significance, that the distribution of grades isuniform.
Three cards are drawn from an ordinary deck of playing cards, with replacement, and the number Y of spades is recorded. After repeating the experiment 64 times, the following outcomes were recorded.
Three marbles are selected from an urn containing 5 red marbles and 3 green marbles. After recording the number X of red marbles, the marbles are replaced in the urn and the experiment repeated 112
A coin is thrown until a head occurs and the number X of tosses recorded. After repeating the experiment 256 times, we obtained the following results. Test the hypothesis at, the 0.05 level of
In Exercise 1.18, test the goodness of fit between the observed class frequencies and the corresponding expected frequencies of a normal distribution with p = 65 and a = 21, using a 0.05 level of
In Exercise 1.19, test the goodness of fit between the observed class frequencies and the corresponding expected frequencies of a normal distribution with p = 1.8 and a = 0.4, using a 0.01 level of
In an experiment to study the dependence of hypertension on smoking habits, the following data were taken on 180 individuals. Test the hypothesis that the presence or absence of hypertension is
A random sample of 90 adults is classified according to gender and the number of hours they watch Use a 0.01 level of significance and test the hypothesis that the time spent watching television is
A random sample of 200 married men all retired was classified according to education and number of children. Test the hypothesis, at the 0.05 level of significance, that the size of a family is
A criminologist conducted a survey to determine whether the incidence of certain types of crime varied from one part of a large city to another. The particular crimes of interest were assault,
A college infirmary conducted an experiment to determine the degree of relief provided by three cough remedies. Each cough remedy was tried on 50 students and the following data recorded. Test the
To determine current attitudes about prayers in public schools, a survey was conducted in 4 Virginia counties. The following table gives the attitudes of 200 parents from Craig County, 150 parents
According to a Johns Hopkins University study published in the American Journal of Public Health, widows live longer than widowers. Consider the following survival data collected on 100 widows and
The following responses concerning the standard of living at the time of an independent opinion poll of 1000 households versus one year earlier seems to be in agreement with the results of a study
A survey was conducted in Indiana, Kentucky, and Ohio to determine the attitude of voters concerning school busing. A poll of 200 voters from each of these states yielded the following results. At
A survey was conducted in two Virginia cities to determine voter sentiment for two gubernatorial candidates in an upcoming election. Five hundred voters were randomly selected from each city and the
In a study to estimate the proportion of wives who regularly watch soap operas, it is found that 52 of 200 wives in Denver. 31 of 150 wives in Phoenix and 37 of 150 wives in Rochester watch at least
A geneticist is interested in the proportion of males and females in a population that have a certain minor blood disorder. In a random sample of 100 males, 31 are found to be afflicted, whereas only
Consider the situation of Exercise 10.54. Oxygen consumption in ml/kg/min was also measured on the nine subjects. It is conjectured that the oxygen consumption should bo higher in an environment
State the null and alternative hypotheses to be used in testing the following claims and determine generally where the critical region is located:(a) The mean snowfall at Lake George during the month
A study was made to determine whether more Italians than Americans prefer white champagne to pink champagne at weddings. Of the 300 Italians selected at random, 72 preferred white champagne, and of
In a set of data analyzed by the Statistics Consulting Center at Virginia Polytechnic Institute and State University (VPI&SU), a group of subjects was asked to complete a certain task on the
State the null and alternative hypotheses to be used in testing the following claims, and determine generally where the critical region is located:(a) At most, 20% of next year's wheat, crop will be
If a can containing 500 nuts is selected at random from each of three different distributors of mixed nuts and there are, respectively, 345, 313, and 359 peanuts in each of the cans, can we conclude
Z-value for testing p1 - p2 = d0: To test the null hypothesis Ho that p1?- p2 = do, where do ? 0, we base our decision on which is a value of a random variable whose distribution approximates the
A study was made to determine whether there is a difference between the proportions of parents in the states of Maryland (MD), Virginia (VA), Georgia (GA), and Alabama (AL) who favor placing Bibles
A study was conducted at the Virginia- Maryland Regional College of Veterinary Medicine Equine Center to determine if the performance of a certain type of surgery on young horses had any effect on
A study was conducted at the Department of Health and Physical Education at Virginia Polytechnic Institute and State University to determine if 8 weeks of training truly reduces the cholesterol
In a study conducted by the Department of Mechanical Engineering and analyzed by the Statistics Consulting Center at the Virginia Polytechnic Institute and State University, the steel rods supplied
In a study conducted by the Water Resources Center and analyzed by the Statistics Consulting Center at the Virginia Polytechnic Institute and State University, two different wastewater treatment
The following data show the number of defects in 100,000 lines of code in a particular type of software program made in the United States and Japan. Is there enough evidence to claim that there is a
Studies show that the concentration of PCBs is much higher in malignant breast tissue than in normal breast tissue. If a study of 50 women with breast cancer reveals an average PCB concentration of
Classify the following random variables as discrete or continuous:X: the number of automobile accidents per year in Virginia.Y: the length of time to play 18 holes of golf. M: the amount of milk
An overseas shipment of 5 foreign automobiles contains 2 that have slight paint blemishes. If an agency receives 3 of these automobiles at random, list the elements of the sample space S using the
Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and to each sample
A coin is flipped until 3 heads in succession occur. List only those elements of the sample space that require 6 or less tosses. Is this a discrete sample space? Explain.
Determine the value c so that each of the following functions can serve as a probability distribution of the discrete random variable X:(a) f(x) = c (x2 + 4), for a: = 0, 1, 2, 3;(b) f(x) =
The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function Find the probability that a bottle of this medicine will have a shell life of(a)
The total number of hours, measured in units of 100 hours that a family runs a vacuum cleaner over a period of one year is a continuous random variable X that has the density function Find the
Find the probability distribution of the random variable W in Exercise 3.3, assuming that the coin is biased so that a head is twice as likely to occur as a tail.
The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function(a) Show that P(0 (b) Find the probability that more than 1/4
Find a formula for the probability distribution of the random variable X representing the outcome when a single die is rolled once.
A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of; 3 of the sets. If x is the number of defective sets purchased by the hotel, find the probability
An investment firm offers its customers municipal bonds that mature after varying numbers of years. Given that the cumulative distribution function of T, the number of years to maturity for a
The probability distribution of A, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given by Construct the cumulative distribution function ofX.
The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function Find the probability of waiting less than 12
Find the cumulative distribution function of the random variable X representing the number of defectives in Exercise 3.11. Then using F(x), find(a) P(X = 1);(b) P(0 < X < 2).
Construct a graph of the cumulative distribution function of Exercise 3.15.
A continuous random variable X that can assume values between x = 1 and x = 3 has a density function given by f(x) = 1/2.(a) Show that the area under the curve is equal to 1.(b) Find P(2 < X <
A continuous random variable X that can assume values between x = 2 and x = 5 has a density function given by f(x) = 2(1 + x)/27. Find(a) P(X < 4);(b) P(3 < X < 4).
For the density function of Exercise 3.17, find F(x). Use it to evaluate P(2 < X < 2.5).
For the density function of Exercise 3.18, find F(x), and use it to evaluate P(3 < X < 4).
Consider the density function(a) Evaluate k.(b) Find F(x) and use it to evaluate P(0.3
Three cards are drawn in succession from a deck without replacement. Find the probability distribution for the number of spades.
Find the cumulative distribution function of the random variable W in Exercise 3.8. Using F(w), find(a) P (W > 0);(b) P (– l < W < 3).
Find the probability distribution for the number of jazz CDs when 4 CDs are selected at random from a collection consisting of 5 jazz CDs, 2 classical CDs, and 3 rock CDs. Express your results by
From a box containing 4 dimes and 2 nickels, 3 coins are selected at random without replacement. Find the probability distribution for the total T of the 3 coins. Express the probability distribution
From a box containing 4 black balls and 2 green balls, 3 balls are drawn in succession, each ball being replaced in the box before the next draw is made. Find the probability distribution for the
The time to failure in hours of an important piece of electronic equipment used in a manufactured DVD player has the density function(a) Find F(x).(b) Determine the probability that the component
A cereal manufacturer is aware that the weight of the product in the box varies slightly from box to box. In fact, considerable historical data has allowed the determination of the density function
An important factor in solid missile fuel is the particle size distribution. Significant problems occur if the particle sizes are too large. From production data in the past, it has been determined
Measurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error and statisticians spend a great deal of time modeling these
Based on extensive testing, it is determined by the manufacturer of a washing machine that the time Y (in years) before a major repair is required is characterized by the probability density
The proportion of the budgets for a certain type of industrial company that is allotted to environmental and pollution control is coming under scrutiny. A data collection project determines that the
Suppose a special type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The pdf that characterizes the proportion Y that
Magnetron tubes are produced from an automated assembly line. A sampling plan is used periodically to assess quality on the lengths of the tubes. This measurement is subject to uncertainty. It is
Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20 second time period, is characterized by the following discrete
On a laboratory assignment, if the equipment is working, the density function of the observed outcome, X is (a) Calculate P(X? (b) What is the probability that X will exceed 0.5? (c) Given that X
Determine the values of c so that the following functions represent joint probability distributions of the random variables A" and Y: (a) f(x, y) — cxy, for x = 1, 2, 3; y = 1, 2, 3;(b) f(x, y) =
If the joint probability distribution of X and Y is given by f (x, y) = x + y /030 for = o, 1, 2, 3; y = (1, 1, 2, find(a) P(X <2, Y = 1);(b) P(X > 2, Y < 1);(c) P(X > Y);(d) P(X + Y = 4).
From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4 pieces of fruit is selected. If X is the number of oranges and Y is the number of apples in the sample:,
A privately owned liquor store operates both a drive-in facility and a walk-in facility. On a randomly selected day, let A" and Y, respectively, be the proportions of the time that the drive-in and
A candy company distributes boxes of chocolates with a mixture of creams, toffees, and cordials. Suppose that the weight of each box is 1 kilogram, but the individual weights of the creams, toffees,
Let X and Y denote the lengths of life, in years, of two components in an electronic system. If the joint density function of these variables is find P(0 < X < 1 \Y = 2).
Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (°F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have
Each rear tire on an experimental airplane is supposed to be filled to a pressure of 40 pound per square inch (psi). Let X denotes the actual air pressure for the right tire and Y denotes the actual

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