The probability density function of the weight of packages delivered by a post office is f (x) = 70 / (69x 2 ) for 1 < x < 70 pounds. (a) Determine the mean and variance of weight. (b) If the...
Consider the endothermic reactions given below. Let A denote the event that a reaction's final temperature is 271 K or less. Let B denote the event that the heat absorbed is above target. Determine...
An article in Nature Genetics [Treatment-specifi c Changes in Gene Expression Discriminate in Vivo Drug Response in Human Leukemia Cells (2003, Vol. 34(1), pp. 8590)] studied gene expression as a...
An article in Nature describes an experiment to investigate the effect on consuming chocolate on cardiovascular health (Plasma Antioxidants from Chocolate, 2003, Vol. 424,). The experiment consisted...
An article in Industrial Quality Control (1956) describes an experiment to investigate the effect of two factors (glass type and phosphor type) on the brightness of a television tube. The response...
Power is the probability of rejecting the null hypothesis when ____.
A scientific supply company has developed a new breed of lab rat, which it claims weighs the same as the classic white rat. The population mean (and standard deviation) for the classic white rat is...
Consider the following computer output for one replicate of a 2 4 factorial experiment. (a) What effects are used to estimate error? (b) Calculate the entries marked with ? in the output. Estimated...
The 95% confidence interval for the difference between population means estimates how ____ or how ____ the difference between the population means might be.
An article in Solid State Technology (1984, Vol. 29, pp. 281284) described the use of factorial experiments in photolithography, an important step in the process of manufacturing integrated circuits....
If the 95% confidence interval for the difference between population means is wide, a reasonable suggestion is to ____ the study with a larger ____.
The sources of variability in an ANOVA are listed in the ____ column of an ANOVA summary table.
SS Total can be broken down into two components: ____ and ____.
If F = F cv , the null hypothesis is ____.
The denominator degrees of freedom for a between-subjects, one-way ANOVA F ratio is df ____.
The alternative hypothesis says that at least ____ population mean is different from at least ____ other population mean.
When treatment has a large impact, there is a lot of variability between group ____.
In their book Introduction to Time Series Analysis and Forecasting (Wiley, 2008), Montgomery, Jennings, and Kulahci presented the data on the drowning rate for children between one and four years old...
Making a sample more homogeneous ____ within-group variability.
A ____ is used to find out which pairs of means in an ANOVA are statistically significantly different.
Complete this ANOVA summary table: Source of Sum of Degrees of Mean Variability Squares Freedom Square Fratio Between 47,843.15 3 groups Within 3,053.88 30 groups Total 50,897.03 33
If SS Within = 168.43 and SS Between = 764.13, what is SS Total ?
A biomedical engineer compared the abrasion resistanceas measured by number of rotations until failureof three different artificial hips. Manufacturer X makes hip joints out of metal, manufacturer Y...
The HSD test is used to determine which pairs of means have a ____ difference.
To find a q value, one needs to know df Within and ____.
____ is used as the effect size in between-subjects, one-way ANOVA.
The numbers in parentheses when reporting the results of a between-subjects, one-way ANOVA in APA format are ____ and ____.
An article in Growth: A Journal Devoted to Problems of Normal and Abnormal Growth [Comparison of Measured and Estimated Fat-Free Weight, Fat, Potassium and Nitrogen of Growing Guinea Pigs (1982, Vol....
Suppose that of 1000 customers surveyed, 850 are satisfied or very satisfied with a corporations products and services. (a) Test the hypothesis H 0 : p = 0.9 against H 1 :p 0.9 at = 0.05. Find the...
If SS Columns = 17.91 and SS Total = 783.54, (a) Calculate 2 Columns and (b) Classify the effect as small, medium, or large.
An article in Technometrics (1999, Vol. 41, pp. 202211) studied the capability of a gauge by measuring the weights of two sheets of paper. The data follow. (a) Check the assumption that the data from...
If F cv Rows is 3.295, what is the decision rule for the rows effect?
An article in Technometrics by S. C. Narula and J. F. Wellington [Prediction, Linear Regression, and a Minimum Sum of Relative Errors (1977, Vol. 19)] presents data on the selling price and annual...
Given M X = 16.33 and M Y = 14.00, calculate deviation scores for X and Y. X ........................ Y 18 ....................... 7 8 ....................... 11 23 ..................... 24
Consider the regression model fit to the arsenic data in Exercise 12-16. Use arsenic in nails as the response and age, drink use, and cook use as the regressors. (a) Calculate 99% confidence...
A article in the Journal of Quality in Clinical Practice [The Application of Statistical Process Control Charts to the Detection and Monitoring of Hospital-Acquired Infections, (2001, Vol. 21, pp....
The following table shows data on gender (coded as 1 = female, 2 = male) and preferred type of chocolate (coded as 1 = white, 2 = milk, 3 = dark) for a sample of 10 students. The students teacher...
The following data show the number of components (per square inch, in millions) being packed on a Pentium-type chip, for years 1994 to 2015. Let x be the number of years since 1994 (e.g., x = 0 for...
A statistics teacher looked out at her class of 32 students and noted that 21 of them were female. Assuming there are equal numbers of males and females in the world, what test should this teacher...
Given this matrix, how many degrees of freedom are there for this chi-square goodness of- fit test?
Given N = 182 and the expected percentages below, find the expected frequencies: C 48% A 14% B 38%
For the random variables X and Y whose joint density function is given in Exercise 2.32 on page 72, find the covarianc Exercise 2.32 A fast-food restaurant operates both a drive through facility and...
A survey conducted at a midwestern university and involving 1,500 students found that 68% had taken out a student loan to help pay for the cost of their college education. A similar study at a...
A developmental psychologist has a teacher rate the boys in his class in terms of how helpful they are. He then classifies the boys as to whether they were ever Boy Scouts or not and compares the...
An economist wondered if job satisfaction was associated with salary. She obtained a sample of first-year teachers from all around the country and found each ones salary, adjusted for the local cost...
A real estate company wondered why some of its agents were more successful than others. They classified their agents as high-volume producers, medium-volume producers, and low-volume producers. All...
A political analyst wishes to select a sample of n = 20 people from a population of 2000. Use the random number table to identify the people to be included in the sample.
Construct the log-likelihood function for the model logit[(x)] = + x with independent binomial outcomes of y 0 successes in n 1 trials at x = 0 and y 1 successes in n 1 trials at x = 1. Derive the...
You notice that some bus riders wear headphones while others do not, but with so many passengers on so many different buses, it is hard to estimate if gender is a factor when it comes to wearing or...
The measure of association lambda for nominal variables (Goodman and Kruskal 1954) has V(Y) = 1 max{ +j } and V(Y|i) = 1 rnax j { j|i }. Interpret lambda as a proportional reduction in prediction...
Organophosphate (OP) compounds are used as pesticides. However, it is important to study their effect on species that are exposed to them. In the laboratory study Some Effects of Organophosphate...
A professor of education was curious about students expectations of academic success. She obtained a sample of college students at the start of their college careers and asked them what they thought...
Suppose P(A) = 1/2, P(B c |AC) = 1/3 and P(C|A) = 1/4. Find P(ABC).
Given the cell means, row means, and column means below, (a) Graph the results to determine if there is an interaction; (b) Speculate about which effects would be statistically significant; (c)...
There are 17 participants in each cell. Each cell is an independent sample. The design is fully crossed. The value in each cell is the cell mean. Calculate (a) Row means and (b) Column means for this...
For the horseshoe crab data, fit a model using weight and width as predictors. Conduct (a) A likelihood-ratio test of H 0 : 1 = 2 , = 0, (b) Separate tests for the partial effects. Why does neither...
An addictions researcher wants to see if male and female alcoholics differ in the type of alcohol they consume. She goes to a large alcohol detox facility, gets a sample of men and a sample of women,...
According to the U.S. government, 68% of American adults weigh more than they should. A dietician, Dr. Christiansen, maintained a theory that drinking 8 or more glasses of water a day was associated...
A researcher on superstition decided to investigate if walking under a ladder really brought about bad luck. He took 100 people to his laboratory, one at a time. As each person entered, he flipped a...
The most common marital status among 50-year-old men living in Rhode Island Select the appropriate statistical technique from among the options in the following figure. Selecting the correct...
The average salary for the first-year teachers in Exercise 16.16 Select the appropriate statistical technique from among the options in the following figure. Data from exercise 16.16 Determine if the...
A demographer was curious if an age difference existed between men and women who were getting married for the first time. From wedding announcements in local papers throughout the United States, he...
Students often gain a few pounds when they move away to college and start eating institutional food. A nutritionist weighed first-year students at the start of the semester, right before...
A dentist wanted to examine if milk consumption as a child had an impact on the need for dentures by age 50. He classified his patients as having consumed a lot of milk as a child (yes vs. no) and as...
A textbook publisher calculated the percentage of deadlines met by each of its authors. It then classified the authors as having made money for the company, broken even, or lost money for the...
An anti-doping agency decided to investigate if an athletes eliteness was related to the likelihood of doping. It unexpectedly drug-tested the top 10 finishers in all the track and field events at a...
Some people like cats and some like dogs. Cats are generally thought of as more independent and aloof. A personality psychologist wondered if a relationship existed between the personality trait of...
The table lists the life (in months) of service before failure of a color television circuit board for 8 television sets manufactured by firm A and 10 sets manufactured by firm B. Use the Wilcoxon...
Let In each case, find an elementary matrix E that satisfies the given equation. EA = C 2 -1 -1 B = -1 1 C = D = -3 -1 3 2 1 -1 -1 || A/
In his autobiography A Sort of Life, British author Graham Greene described a period of severe mental depression during which he played Russian Roulette. This games consists of putting a bullet in...
Find a (real) general solution. State which rule you are using. Show each step of your work. 10y" + 50y' + 57.6y = cos x
Three components are randomly sampled, one at a time, from a large lot. As each component is selected, it is tested. If it passes the test, a success (S) occurs; if it fails the test, a failure (F)...
Let and Use the matrix-column representation of the product to write each column of AB as a linear combination of the columns of A. -2 A = -3 2 0 -1 3 0 B = -1 6. 4.
If {v 1 ,v 2 ,.........v n } is an orthonormal basis for R n and A = c 1 v 1 v T 1 + c 2 v 2 v T 2 +..........+ c n v n v T n Prove that A is a symmetric matrix with eigenvalues c 1 , c 2 ,......c n...
Simulate the dice game in Example 4.3. Estimate the expectation and variance of your winnings. Data from Example 4.3. Let X ¼ Unif{1, . . . , n}. The expectation of X is (+1)) n +1 -P(X - )...
A random variable X has density function proportional to x 5 for x > 1. (a) Find the constant of proportionality. (b) Find and graph the cdf of X. (c) Use the cdf to find P(2 < X < 3). (d) Find the...
It is 9:00 p.m. The time until Joe receives his next text message has an exponential distribution with mean 5 minutes. (a) Find the probability that he will not receive a text in the next 10 minutes....
Find the probability that an exponential random variable is within two standard deviations of the mean. That is, compute P(|X | 2), where = E[X] and = SD[X].
The manufacture of a certain part requires two different machine operations. The time on machine 1 has mean 0.5 hours and standard deviation 0.4 hours. The time on machine 2 has mean 0.6 hours and...
Suppose X has density function
Let (X, Y, Z) be uniformly distributed on a three-dimensional box with side lengths 3, 4, and 5. Find P(X < Y < Z).
The time each student takes to finish an exam has an exponential distribution with mean 45 minutes. In a class of 10 students, what is the probability that at least one student will finish in less...
Let X and Y have joint density (a) By examining the joint density function can you guess the conditional density of X given Y = y? (Treat y as a constant.) Confirm your guess. (b) Similarly, first...
Sound City sells the TrueSound-XL, a top-of-the-line satellite car radio. Over the last 100 weeks, Sound City has sold no radios in three of the weeks, one radio in 20 of the weeks, two radios in 50...
Data 1.1 introduced the dataset StudentSurvey, and Example 1.2 identified seven of the variables in that dataset as categorical or quantitative. The remaining variables are: Year...
A recent study examined the impact of the color red on how attractive men perceive women to be. In the study, men were randomly divided into two groups and were asked to rate the attractiveness of...
If investors want portfolios with small risk (variance), should they look for investments that have positive covariance, have negative covariance, or are uncorrelated?
The latest US Census lists the average household size for all households in the US as 2.61. (A household is all people occupying a housing unit as their primary place of residence.) Figure 3.6 shows...
Use StatKey or other technology to generate a sampling distribution of sample means using a sample size of n = 5 from the Points values in Table 3.4 on page 174, which gives the number of points for...
Figure 3.5(a) shows sample proportions from samples of size n = 40 from a population. Figure 3.5a. Refer to the sampling distributions given in Figure 3.5. In each case, estimate the value of the...
The percentage of the population that is less than 25 is closest to: 10% 28% 50% 62% 95% Refer to the density function shown in Figure 5.11. In each exercise, use the density function to choose the...
In Exercise 6.128, we see that plastic microparticles are contaminating the worlds shorelines and that much of the pollution appears to come from fibers from washing polyester clothes. The same study...
If airplanes A and B are moving southwest with speed |v A | = 550 mph, and northwest with speed |v B | = 450 mph, respectively, what is the relative velocity v = v B - v A of B with respect to A?
Determine the principal value of the argument and graph it as in Fig. 325. -1 + 0.1i, -1 - 0.1i pl+i /4
Estimate the answer. The total weight of three people on an elevator if their weights are 95 lb, 127 lb, and 210 lb.
Suppose that past experience shows that about 10% of passengers who are scheduled to take a particular flight fail to show up. For this reason, airlines sometimes overbook flights, selling more...
From its founding through 2012, the Rock and Roll Hall of Fame has inducted 273 groups or individuals. Table 11.4 shows how many of the inductees have been female or have included female members and...
The difference of any two counting numbers will be a counting number. Find a counterexample to show that each statement is incorrect.
The dataset HollywoodMovies2011 contains information on all 136 movies to come out of Hollywood in 2011. We see in Exercise B.13 that 27 of the movies were comedies. If we take 1000 samples of size n...
Graph a sample space for the experiments: Rolling a die until the first Six appears