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probability statistics
Probability And Statistics For Engineers And Scientists 9th Edition Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying E. Ye - Solutions
For a given variable, all data for that variable are entered into a single column in the Data View tab.a. True, all data for that variable are entered into a single column in the Data View tab.b. False, data should always be entered in the Variable View tab.
Using SPSS, which options in the menu bar do you select to construct a frequency distribution for quantitative data?a. Analyze, then Descriptive Statistics and Exploreb. Analyze, then Descriptive Statistics and Descriptivesc. Analyze, then Descriptive Statistics and Frequencies
A student, Jasmine, scores in the 80th percentile on an exam. Which of the following correctly explains what this means?a. 80% of students scored higher on the exam than Jasmine.b. Jasmine scored higher than 80% of all others who took the same exam?
A ______ is the value of a score on a measurement scale below which a specified percentage of scores in a distribution fall. The corresponding percentile of a percentile point is the ______ of that score. [Fill in the blanks]a. percentile point; percentile rankb. percentile rank; percentile point
What type of distribution is used to identify percentiles, which are measures of the relative position of individuals or scores within a larger distribution?a. simple frequency distributionb. cumulative frequency distributionc. cumulative percentage distribution
A study evaluating consumer behavior classifies products being studied as either tangible goods or services. Out of 60 total products, 15 were classified as tangible goods. The relative frequency for services is equal toa. .15b. .25c. .60d. .75
The sum of relative frequencies across all intervals is equal toa. the total frequency countb. 100%c. 1.00
Why do researchers often choose to construct a relative frequency distribution to summarize data?a. To summarize the total frequencies in a distribution.b. To summarize relatively small data sets.c. To summarize large data sets.
In which direction do we summarize data in a cumulative frequency distribution when we want to describe data as “at or above” a given score?a. Top downb. Bottom up
In which direction do we summarize data in a cumulative frequency distribution when we want to describe data as “at or below” a given score?a. Top downb. Bottom up
An open interval can make it less obvious that an outlier exists in a data set.a. Trueb. False
A set of scores ranges between 4 and 23. What is the interval width for a simple frequency distribution if you choose to create 5 intervals?a. 23/5 = 4.6b. 20/5 = 4.0c. 19/5 = 3.8
A researcher observes that a single parent works 42.25 hours per week. The degree of accuracy of 42.25 isa. the ones placeb. the tenths placec. the hundredths place
Which of the following is a summary display for a distribution of data organized or summarized in terms of how often (or frequently) scores occur?a. open intervalb. boundariesc. frequency distribution
Summarizing the frequency of scores in a distribution can be more valuable for ____ data sets. [Fill in the blank]a. smallerb. relativec. larger
A study shows that out of 50 employees, 70% reached their sales goals following a training seminar. Thus, the frequency of those reaching their sales goal isa. 35 employeesb. 40 employeesc. 50 employeesd. 70 employees
Which of the following explains why is it valuable to summarize data?a. It can increase the complexity of very large data sets.b. It can make the presentation and interpretation of a distribution of data clearer.
A researcher observes patrons at a sporting event and compares differences in social interactions between the “home team” and the “away team” fans. Assuming that a patron could not be both a home team and an away team fan, which of the following is true for entering these data into SPSS?a.
Which of the following statements is true for entering data into SPSS?a. When different participants are observed in each group, we code the grouping variable.b. When entering data into SPSS, we enter data by column when the same participants are observed in each group.c. Both a and b are correct.
Recording which friend students study with describes ____ types of data, whereas recording the number of hours spent studying per week describes ____ types of data.[Fill in the blanks]a. qualitative; quantitativeb. quantitative; qualitativec. qualitative; discreted. quantitative; continuous
The data for which type of variables are often subjected to statistical analysis?a. quantitativeb. qualitative
The procedure of converting a categorical variable to numeric values is called:a. codingb. pilotingc. constructing
In the published literature, rating scales—which are widely used in the behavioral sciences—are typically treated as ____ scale measures. [Fill in the blank]a. nominalb. ordinalc. intervald. ratio
The correlational method does not control the conditions under which observations are made.
A correlation identifies whether changes in one variable cause changes in a second variable.
For Questions 17 and 18, identify whether the variable described is an independent variable or a dependent variable for an experiment. Answer I for an independent variable and D for a dependent variable.Suppose a researcher records differences in cell phone use during class between students who are
For Questions 17 and 18, identify whether the variable described is an independent variable or a dependent variable for an experiment. Answer I for an independent variable and D for a dependent variable.A researcher records differences in attention between students who drink coffee and those who do
For Questions 17 and 18, identify whether the variable described is an independent variable or a dependent variable for an experiment. Answer I for an independent variable and D for a dependent variable.The variable that is manipulated to create the groups.
For Questions 17 and 18, identify whether the variable described is an independent variable or a dependent variable for an experiment. Answer I for an independent variable and D for a dependent variable.The variable measured in each group.
Which of the following is an example of a study that is structured like an experiment?a. A study evaluating the extent to which exercise frequency and self-image are related among college students.b. A study evaluating whether the amount consumed in a buffet differs between participants who are
A researcher tests the effectiveness of a new drug treatment by randomly assigning participants to a group that receives the drug treatment or to a control group where a placebo (i.e., fake) drug is administered. What type of research method is described in this example?a. experimentalb.
A psychologist reviews notes for all of their patients and determines that on average, patients complete therapy in 24 days. The average time to complete therapy among all their patients is called aa. sample statisticb. population parameter
Researchers measure ____ in a sample to learn more about ____ in the larger population of interest. [Fill in the blanks]a. statistics; parametersb. parameters; statistics
A statistics class has 25 students enrolled, but only 23 students attended class. In this class, which value represents the population of students enrolled?a. 23b. 25
A researcher is interested in sampling students to participate in a study on learning and memory. Which of the following describes the procedures the researcher would use to select a sample?a. The researcher identifies the population of students, then selects a portion of them to participate in the
Descriptive statistics can be used to describe populations and samples of data.
Graphs, tables, and summary statistics all illustrate the application of inferential statistics.
Which of the following best explains what it means to “be a critical consumer” of statistical information?a. It means that you can critically evaluate statistical information to distinguish between appropriate and misleading statistics.b. It means that you can be critical of all statistics so
Understanding statistics is important in that it allows youa. to be a critical consumer of the information you come acrossb. to be a critical consumer of scientific informationc. Both a and b are correct.
A professor records the number of questions that students ask during class in each class during a semester. Which of the following is the statistic measured in this example?a. the class in which students asked questionsb. the semester in which observations were madec. the number of questions that
A researcher records the value of home prices over a period of years from before to following a recession. Which of the following is the statistic measured in this example?a. yearsb. home pricesc. whether or not there was a recession
Which of the following explains how statistics can be used?a. Statistics can be used to understand and interpret data.b. Statistics can be used to summarize data to make sense of it.c. Both a and b are correct.
Statistics is a branch of mathematics used toa. make inferences about populations based on observations made in samples.b. summarize, analyze, and interpret a group of numbers or observations.c. summarize data measured in samples but not data measured in populations.
Group Project: The class should be divided into groups of four people. The four students in each group should go to the college gym or a local fitness center. The students should ask each person who comes through the door his or her height in inches. Each group will then divide the height data by
Consider the situation in Review Exercise 8.74. Suppose a considerable effort is conducted to “tighten” the variability in the system. Following the effort, a random sample of size 40 is taken from the new assembly line and the sample variance is s= 0.188 ounces . Do we have strong numerical
Suppose a filling machine is used to fill cartons with a liquid product. The specification that is strictly enforced for the filling machine is 9 ± 1.5 oz. If any carton is produced with weight outside these bounds, it is considered by the supplier to be defective. It is hoped that at least 99% of
In Chapter 9, the concept of parameter estimation will be discussed at length. Suppose X is a random variable with meanμ and variance σ = 1.0. Suppose also that a random sample of size n is to be taken and is to be used as an estimate of μ. When the data are taken and the sample mean is
Given a normal random variable X with mean 20 and variance 9, and a random sample of size n taken from the B A A B Bdistribution, what sample size n is necessary in order that
From the information in Review Exercise 8.70, compute(assuming μ = 65%) .
The concentration of an active ingredient in the output of a chemical reaction is strongly influenced by the catalyst that is used in the reaction. It is felt that when catalyst A is used, the population mean concentration exceeds 65%. The standard deviation is known to be σ = 5%. A sample of
Two distinct solid fuel propellants, type A and type B, are being considered for a space program activity. Burning rates of the propellant are crucial. Random samples of 20 specimens of the two propellants are taken with sample means 20.5 cm/sec for propellant A and 24.50 cm/sec for propellant B.
Consider the situation of Review Exercise 8.62. If the population from which the sample was taken has population mean μ = 53, 000 kilometers, does the sample information here seem to support that claim? In your answer, compute and determine from Table A.4 (with 9 d.f.) whether the computed t-value
The breaking strength X of a certain rivet used in a machine engine has a mean 5000 psi and standard deviation 400 psi. A random sample of 36 rivets is taken. Consider the distribution of , the sample mean breaking strength.1. What is the probability that the sample mean falls between 4800 psi and
Consider Review Exercise 8.56. Comment on any outliers in the data.1 2
Consider Example 1.5 on page 45. Comment on any outliers.
If and represent the variances of independent random samples of size n = 16 and n = 27, taken from normal populations with variances and , respectively, find
Consider the data of Exercise 1.19 on page 51. Construct a box-and-whisker plot. Comment. Compute the sample mean and sample standard deviation.
A taxi company tests a random sample of 10 steel-belted radial tires of a certain brand and records the following tread wear: 48,000, 53,000, 45,000, 61,000, 59,000, 56,000, 63,000, 49,000, 53,000, and 54,000 kilometers. Use the results of Exercise 8.14 on page 251 to find the standard deviation of
The number of destructive tsunami that originate in the Pacific basin each year is a random variable having a Poisson distribution, with μ = 2 per year. Find the probability that this area will be hit by 1. exactly 5 tsunami in 2 years;2. at most 3 tsunami in 2 years.1 2
The price quotations for a home appliance is collected randomly from five different retail shops in a city. These are$305, $312, $296, $304, and $307. Find the variance of the quoted prices.
If and represent the variances of independent random samples of size n = 8 and n = 12, taken from normal populations with equal variances, find .
In testing for carbon monoxide in a certain brand of cigarette, the data, in milligrams per cigarette, were coded by subtracting 12 from each observation. Use the results of Exercise 8.14 on page 251 to find the standard deviation for the carbon monoxide content of a random sample of 15 cigarettes
If X , X , …, X are independent random variables having identical exponential distributions with parameter θ, show that the density function of the random variable Y = X +X +⋯+X is that of a gamma distribution with parameters α = n and β = θ.1 2 n 1 2 n
Consider the data displayed in Exercise 1.20 on page 51.Construct a box-and-whisker plot and comment on the nature of the sample. Compute the sample mean and sample standard deviation.
Construct a normal quantile-quantile plot of these data, which represent the diameters of 36 rivet heads in 1/100 of an inch:Review Exercises
Construct a quantile plot of these data, which represent the lifetimes, in hours, of fifty 40-watt, 110-volt internally frosted incandescent lamps taken from forced life tests:
Consider the following measurements of the heatproducing capacity of the coal produced by two mines (in millions of calories per ton):Can it be concluded that the two population variances are equal?
Pull-strength tests on 10 soldered leads for a semiconductor device yield the following results, in pounds of force required to rupture the bond:0.01 1 2 0.01 1 2 0.05 1 2 0.95 1 2 0.99 1 2 Another set of 8 leads was tested after encapsulation to determine whether the pull strength had been
For an f-distribution, find 1. f , when v = 12 and v = 10.2. f , when v = 10 and v = 12.3. f , when v = 15 and v = 8.4. f , when v = 10 and v = 5.5. f , when v = 18 and v = 14.
A transport company claims that the average running time for a bus on a particular route is 300 minutes. Six buses are randomly observed and their running times are recorded as follows: 320, 310, 295, 312, 302, and 308 minutes. Would you agree with the transport company’s claim? Assume a normal
A normal population with unknown variance has a mean of 15. Is one likely to obtain a random sample of size 16 from this population with a mean of 18 and a standard deviation of 3.8? If not, what conclusion would you draw?
A technical training firm claims that the average time for their trainees to master a particular skill is 40 hours. To maintain this average, 24 students are tested every month. If the computed t-value falls between –t and t , the firm is satisfied with its claim. What conclusion should the firm
Given a random sample of size 30 from a normal distribution, find k such that, 1. P(–1.699 < T < k) = 0.945;2. P(k < T < 2.045) = 0.025;3. P(–k < T < k) = 0.98.
1. Find P(–t < T < t ).2. Find P(–t > T > t ).
1. Find P(T < 2.65), when v = 13.2 22 22 22 2 0.05 0.05 0.95 2. Find P(T > 2.06), when v = 25.3. Find P(–1.74 < T < 2.567), when v = 17.4. Find P(T > –2.06), when v = 25.
1. Find t , when v = 16.2. Find –t , when v = 12.3. Find t , when v = 9.
Show that the variance of S for random samples of size n from a normal population decreases as n becomes large. [Hint:First find the variance of (n – 1)S /σ .]
The scores on a placement test given to college freshmen for the past five years are approximately normally distributed with a mean μ = 74 and a variance σ = 8. Would you still consider σ = 8 to be a valid value of the variance if a random sample of 20 students who take the placement test this
Assuming that the sample variances are continuous measurements, find the probability that a random sample of 30 observations, from a normal population with variance σ = 5, will have a sample variance of S that is 1. greater than 7.338;2. between 2.766 and 7.883.
For a chi-square distribution, find , such that 1.2.3.
For a chi-square distribution, find , such that 1.2.3.
For a chi-square distribution, find 1.2.3.
For a chi-square distribution, find 1.2.3.
Let X , X , …, X be a random sample from a distribution that can take on only positive values. Use the Central Limit Theorem to produce an argument that if n is sufficiently large, then Y = X X … X has approximately a lognormal distribution.
Consider the situation described in Example 8.4 on page 254. Do these results prompt you to question the premise that μ= 800 hours? Give a probabilistic result that indicates how rare an event is when μ = 800. On the other hand, how rare would it be if μ truly were, say, 760 hours?
Two alloys A and B are being used to manufacture a certain steel product. An experiment needs to be designed to compare the two in terms of maximum load capacity in tons(the maximum weight that can be tolerated without breaking).It is known that the two standard deviations in load capacity are
The chemical benzene is highly toxic to humans. However, it is used in the manufacture of many medicine dyes, leather, and coverings. Government regulations dictate that for any production process involving benzene, the water in the output of the process must not exceed 7950 parts per million (ppm)
Two different box-filling machines are used to fill cereal boxes on an assembly line. The critical measurement influenced by these machines is the weight of the product in the A B boxes. Engineers are quite certain that the variance of the weight of product is σ = 1 ounce. Experiments are
Consider Case Study 8.2 on page 258. Suppose 18 specimens were used for each type of paint in an experiment and , the actual difference in mean drying time, turned out to be 1.0.1. Does this seem to be a reasonable result if the two population mean drying times truly are equal? Make use of the
The mean score of the students from training centers for a particular competitive examination is 148, with a standard deviation of 24. Assuming that the means can be measured to any degree of accuracy, what is the probability that two groups selected at random, consisting of 42 and 64 students,
The distribution of the weights of one-week-old chicks of a certain breed has a mean of 120 grams and a standard deviation of 12 grams. The distribution of weights of chicks of the same age of another breed is 92 grams with a standard deviation of 8 grams. Assuming that the sample mean can be
A sample of 30 people is randomly selected from city A, where the average height of adults is 160 centimeters with a standard deviation of 9 centimeters. A second random sample of size 42 is selected form city B, where the average height of adults is 158 centimeters with a standard deviation of 10
In a chemical process, the amount of a certain type of impurity in the output is difficult to control and is thus a random variable. Speculation is that the population mean amount of the impurity is 0.20 gram per gram of output. It is known that the standard deviation is 0.1 gram per gram. An
The amount of time that a vehicle spends in a petrol bunk is a random variable with the mean μ = 4.5 minutes and a standard deviation σ = 1.8 minutes. If a random sample of 24 vehicles is observed, find the probability that its mean time at the petrol bunk is 1. at most 3.6 minutes;2. more than
The average time taken to complete a project in a real estate company is 18 months, with a standard deviation of 3 months. Assuming that the project completion time approximately follows a normal distribution, find 21. the probability that the mean completion time of 4 such projects falls between
The random variable X, representing the number of cherries in a cherry puff, has the following probability distribution:1. Find the mean μ and the variance σ of X.2. Find the mean and the variance of the mean for random samples of 36 cherry puffs.3. Find the probability that the average number of
The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. Suppose 200 random samples of size 25 are drawn from this population and the means recorded to the nearest tenth of a centimeter. Determine 1. the mean
A soft-drink machine is regulated so that the amount of drink dispensed averages 240 milliliters with a standard deviation of 15 milliliters. Periodically, the machine is checked by taking a sample of 40 drinks and computing the average content. If the mean of the 40 drinks is a value within the
Given the probability mass function of the results of 72 independents tosses of an unbiased die find the probability that it will yield a sample mean greater than 3.5 but less than 4.0. Assume the means are measured to the nearest tenth.
A certain type of automobile battery has a mean life of 1500 days and standard deviation of 250 days. How does the variance of the sample mean change when the sample size is 1. increased from 49 to 625?2. decreased from 625 to 25?
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