We are given m data points and we seek an hyperplane where and that best fits the given points, in the sense of a minimum sum of squared distances criterion. Formally, we need to solve the...
Find the centre and the radius of each of the following circles. a. x 2 + y2 = 16 b. 2x 2 + 2y2 = 9 c. x 2 + (y 2) 2 = 25 d. (x 5) 2 + (y + 3) 2 = 4 e. (x + 7) 2 + y 2 = 18 f. 2(x 3) 2 + 2(y + 4)...
Paint is poured onto a flat surface and a circular patch is formed. The area of the patch increases at a rate of 5cm 2 s 1 . a. Find, in terms of , the radius of the patch after 8 seconds. b. Find,...
The diagram shows a water container in the shape of a triangular prism of length 120 cm. The vertical cross-section is an equilateral triangle. Water is poured into the container at a rate of 24 cm 3...
A demolition ball is used to tear down a building. Its distance s (in m) above the ground as a function of time t (in s) after it is dropped is s = 17.5 4.9t 2 . Because s = f (t), find f(1.2).
Use Figure 2.19 to fill in the blanks in the following statements about the function f at point A. (a) f(_ ) = ___ (b) f'(_ ) = ___ (7,3) (7.2.3.8) Figure 2.19 Tangent line f(x)
Use a calculator or computer to evaluate the integral. 3 4 Ve + zdz
With t in seconds, the velocity of an object is v(t) = 10 + 8t t 2 m/sec. (a) Represent the distance traveled during the first 5 seconds as a definite integral and as an area. (b) Estimate the...
Figure 5.9 shows the velocity of an object for 0 t 6. Calculate the following estimates of the distance the object travels between t = 0 and t = 6, and indicate whether each result is an upper or...
Assume points P and Q are close. Estimate g(Q). P = (30, 125), Q = (25, 135), g(P) = 840, g x (P) = 4,g y (P) = 1.5.
Find a possible formula for the function represented by the data. x 0 f(x) 4.30 1 2 6.02 8.43 3 11.80
Sketch a contour diagram for the function with at least four labeled contours. Describe in words the contours and how they are spaced. f(x, y) = x 2 + y 2
Find the derivative of the functions in Problems. f(x) = 6e 5x + e x2
The vase in Figure 4.31 is filled with water at a constant rate (that is, constant volume per unit time). (a) Graph y = f(t), the depth of the water, against time, t. Show on your graph the points at...
The function f is defined for all x. Use the graph of f' to decide: (a) Over what intervals is f increasing? Decreasing? (b) Does f have local maxima or minima? If so, which, and where? 2 f'(x) 4 X
The function f is defined for all x. Use the graph of f' to decide: (a) Over what intervals is f increasing? Decreasing? (b) Does f have local maxima or minima? If so, which, and where? -1 f'(x) x
For what values of a and b does f(x) = a(x b ln x) have a local minimum at the point (2, 5)? Figure 4.16 shows a graph of f(x) with a = 1 and b = 1. 3 2 1 f(x) = x-lnx 1 2 Figure 4.16 3 X
Let F(x) be an antiderivative of f(x), with F(0) = 50 and 5 0 f(x) dx = 12. What is F(5)?
Table 6.2 shows the monthly change in water stored in Lake Sonoma, California, from March through November 2014. The change is measured in acre-feet per month.1 On March 1, the water stored was...
Find the derivative of the functions in Problems. R = (q 2 + 1) 4
Use the tangent line approximation. Given f(x) = x 4 x 2 + 3 approximate f(1.04).
Use the tangent line approximation. Given f(x) = x 3 + x 2 6, approximate f(0.97).
For the functions in Problems (a) Find the derivative at x = 1. (b) Find the second derivative at x = 1. (c) Use your answers to parts (a) and (b) to match the function to one of the graphs in Figure...
For f(x) = x 2 + 5x +2, find the equation of the tangent line at (a) x = 1 (b) x = 1
(a) Find the equation of the tangent line to f(x) = x 3 at the point where x = 2. (b) Graph the tangent line and the function on the same axes. If the tangent line is used to estimate values of the...
Fill in each blank so that the resulting statement is true. When solving by the addition method, we can eliminate y by multiplying the first equation by 2 and the second equation by________ , and...
Identify a piece of information that you have gained through each of the sources of knowledge discussed in this chapter (superstition and intuition, authority, tenacity, rationalism, empiricism, and...
Organize the data in Exercise 1 into a class interval frequency distribution using 10 intervals with frequency (f) and relative frequency (rf) columns. s8
For the distribution described in exercise 4, what is the probability of selecting someone who is 70 inches or taller or 64 inches or shorter? Data from exercise 4 If height is normally distributed...
In a study on caffeine and stress, college students indicated how many cups of coffee they drink per day and their stress level on a scale of 1 to 10. The data are provided in the following table....
A researcher is interested in whether students who attend private high schools have higher average SAT scores than students in the general population. A random sample of 90 students at a private high...
What is the advantage of manipulating more than one independent variable in an experiment?
A researcher interested in the effects of exercise on stress had participants exercise for 30, 60, or 90 minutes per day. The mean stress level on a 100-point stress scale (with 100 indicating high...
What is the difference between a between- groups research design and a within-groups research design?
What is the geometric mean of LVMI by blood pressure group?
The following statements are wrong but can be corrected by substituting one word or phrase. (See the instructions in Exercise 1.13.) Identify the incorrect word or phrase in each of the following...
Orthostatic hypertension is sometimes defined based on an unusual change in blood pressure after changing position. Suppose we define a normal range for change in systolic blood pressure (SBP) based...
For each variable (other than ID), obtain appropriate descriptive statistics (both numeric and graphic)? Table 2.17: Format for FEV.DAT The data in Table 2.17 are available for each child. Variable...
What is the expected overall CHD mortality rate in Olmstead County in 2015 if these trends continue? The investigators reported that for both men and women, inhospital CHD death rates were declining...
To assess the variability of the assay, the investigators need to compute the coefficient of variation. Compute the coefficient of variation (CV) for each subject by obtaining the mean and standard...
Suppose we know two of the three people have Alzheimers disease. What is the conditional probability that they are both younger than 80 years of age? Mental Health Estimates of the prevalence of...
What is the conditional probability that the woman will be affected given that the man is affected? How does this value compare with the prevalence in Table 3.5? Why should it be the same (or...
What is the probability that at least one member of the couple is affected? Suppose the probability that both members of a married couple, each of whom is 7579 years of age, will have Alzheimers...
Suppose 3 children in a village ages 3, 5, and 7 are vaccinated with the QIV vaccine. What is the probability that at least one child among the 3 will get influenza? Infectious Disease Commonly used...
Suppose 6 of 15 students in a grade-school class develop influenza, whereas 20% of grade-school students nationwide develop influenza. Is there evidence of an excessive number of cases in the class?...
If A, B are two events such that A = {older child is affected}, B = {younger child is affected}, then are the events A, B independent? Genetics Suppose that a disease is inherited via a dominant mode...
What is the probability of obtaining exactly 6 events for a Poisson distribution with parameter = 4.0? Suppose we want to check the accuracy of self-reported diagnoses of angina by getting further...
Find the probability of getting 3 or more episodes of otitis media in the first 2 years of life. Otolaryngology Assume the number of episodes per year of otitis media, a common disease of the middle...
Consider the subgroup of families in which the mother is not a current smoker. What is the probability that the father is a current smoker among such families? How does this probability differ from...
What is the PV of the test? Suppose the self-reports are completely accurate and are representative of the number of eighth-grade students who smoke in the general community. We are considering using...
What is the probability that 0 rats will die in the 8-hour period? Cancer, Epidemiology An experiment is designed to test the potency of a drug on 20 rats. Previous animal studies have shown that a...
What is the sensitivity of the test? Mental Health The Chinese Mini-Mental Status Test (CMMS) consists of 114 items intended to identify people with Alzheimers disease and senile dementia among...
After how many years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females, if the incidence rate remains constant over time? Ophthalmology,...
A sample of 504 patients in early stages of Alzheimers disease is divided into two groups. One group receives an experimental drug; the other receives a placebo. The advance of the disease in the...
A farmer interested in the weight of his soybean crop randomly samples 100 plants and weighs the soybeans on each plant? A research objective is presented. For each, identify the population and...
What is the probability of 0, 1, and 2+ additional pregnancies if the first birth was a stillbirth? Demography A study based on data collected from the Medical Birth Registry of Norway looked at...
To determine the prevalence of human growth hormone (HGH) use among high school varsity baseball players, the State Athletic Commission randomly selects 50 high schools. All members of the selected...
A college official divides the student population into five classes: freshman, sophomore, junior, senior, and graduate student. The official takes a simple random sample from each class and asks the...
What is the probability that exactly two of the two offspring will be affected in a family with dominant disease with complete penetrance? Genetics A dominantly inherited genetic disease is...
To obtain students opinions about proposed changes to course registration procedures, the administration of a small college asked for faculty volunteers who were willing to administer a survey in one...
What is the probability that exactly two of the two offspring will be affected in a family with dominant disease with reduced penetrance? Genetics A dominantly inherited genetic disease is identified...
What is the probability that the mode of transmission for this particular family is dominant with complete penetrance? Is this a prior probability or a posterior probability? Genetics A dominantly...
The county sheriff wants to determine if a certain highway has a high proportion of speeders traveling on it. Design a sampling method to obtain the individuals in the sample. Be sure to support your...
When should relative frequencies be used when comparing two data sets? Why?
The following data represent the number of grams of fat in breakfast meals offered at McDonalds. (a) construct a stem-and-leaf plot and (b) describe the shape of the distribution. 27 25 30 32 12 22...
Suppose that a baby is born with a birth defect, but the babys ancestry is unknown. What is the posterior probability that the baby will have both parents from population A, both parents from...
Why shouldnt classes overlap when summarizing continuous data in a frequency or relative frequency distribution?
What is the sensitivity of this test? Cancer Breast cancer is considered largely a hormonal disease. An important hormone in breast-cancer research is estradiol. The data in Table 3.18 on serum...
Compute the standard deviation and range for the duration of hospitalization for the 25 patients. TABLE 2.13 Hospltal-stay data First Received Duration First WBC Received bacterial Ser (x 10)...
Suppose the man does not run for 6 months over the winter due to snow on the ground. He resumes running once a week in the spring and records a running time = 12.97 minutes in his first week of...
An Uber driver kept track of the number of calls he received over a 28-day period. The data are listed here. Create a histogram. 3 10 10 7 8 11 8 10 7 4 17 13 9 7 12 8 10 4
If the normal range is 65120 mg/dL, then what percentage of values will fall in the normal range? Blood Chemistry In pharmacologic research a variety of clinical chemistry measurements are routinely...
Compute the mean change in cholesterol? Table 2.15: Serum-cholesterol levels (mg/dL) before and after adopting a vegetarian diet *Before after. Subject Before After Difference* 195 146 49 145 155 -10...
What is the probability that the number of cardinal birds will be U at least once on Christmas day during the 10-year period 20122021? The observers wish to identify a normal range for the number of...
Count the number of people assigned to each treatment group. How does this number compare with the expected number in each group? Gastroenterology Suppose we are asked to construct a list of...
Construct a 95% CI for the true mean SBP among people with glaucoma? Ophthalmology, Hypertension A study is conducted to test the hypothesis that people with glaucoma have higher-than-average blood...
If the average SBP for people of comparable age is 130 mm Hg, is there an association between glaucoma and blood pressure? Ophthalmology, Hypertension A study is conducted to test the hypothesis that...
If 500 newborns are screened at the inner-city hospital, then what is the exact binomial probability of exactly 5 HIV-positive test results? Infectious Disease Newborns were screened for human...
Answer Problem 4.14 for a mixed urban/suburban hospital (hospital C). Infectious Disease Newborns were screened for human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS) in...
What does a 95% CI mean, in words, in this case? Suppose we decide a better measure of the effectiveness of the drug is the mean decrease in blood pressure rather than the measure of effectiveness...
What is the probability that among 10 true hypertensives at least 50% are being treated appropriately and are complying with this treatment? Hypertension A national study found that treating people...
If the preceding 50% rates were each reduced to 40% by a massive education program, then what effect would this change have on the overall mortality rate among true hypertensives; that is, would the...
What is the probability that an infant will have one or more episodes of otitis media by the end of the sixth month of life? The first year of life? Pediatrics, Otolaryngology Otitis media is a...
What is the expected number of otitis-prone families of 100 five-sibling families? Pediatrics, Otolaryngology Otitis media is a disease that occurs frequently in the first few years of life and is...
1. Consider the Data Set BONEDEN.DAT at www.cengagebrain.com. Calculate the difference in bone density of the lumbar spine (g/cm 2 ) between the heavier-smoking twin and the lighter-smoking twin...
lf 20 melanoma patients are given lnterleukin-2 plus a vaccine, what is the probability that exactly 5 of them will have a positive response to treatment (either complete or partial response)? Cancer...
lf 20 melanoma patients are given lnterleukin-2 plus a vaccine, what is the probability that at least 3 of them will have a positive response to treatment? Cancer A clinical trial was conducted among...
Determine whether the underlined value is a parameter or a statistic. 1. Following the 2014 national midterm election, 18% of the governors of the 50 United States were female. 2. The average score...
Suppose we observe 30 cases of colon cancer over 35,000 person-years among women ages 5054. Provide a point estimate and 95% CI for the incidence rate of colon cancer in this age-gender group? As an...
State the hypotheses that we can use to answer this question? The standard deviation of daily iron intake in the larger population of 9- to 11-year-old boys was 5.56 mg. We want to test whether the...
Identify the critical t values for each of the following tests: a. A single-sample t test examining scores for 26 participants to see if there is any difference compared to the population, using a p...
Suppose we eventually plan to accumulate 50 MI cases during the period 20102015. Assume that the 24-hour case-fatality rate is truly 20% during this period. How much power would such a study have in...
If we assume that the distribution of is normally distributed, then what is the 90 percentile (i.e., the upper decile) and 10 percentile (i.e., the lower decile) of the distribution? Hypertension A...
Assuming that the duration of smoking is normally distributed, what proportion of men in this age group have smoked for more than 20 years? Cardiovascular Disease, Pulmonary Disease The duration of...
If the clinically desirable range for cholesterol is < 200 mg/dL, what proportion of people have clinically desirable levels of cholesterol? Cardiovascular Disease, Pulmonary Disease The duration of...
Suppose a community has 1000 families living in it. What is the probability that between one and five families are hypertensive? Hypertension People are classified as hypertensive if their systolic...
What is the probability that a 45-year-old man with an FEV of 4.0 L will be functionally impaired by age 75? Pulmonary Disease Forced expiratory volume (FEV) is an index of pulmonary function that...
An excess of lymphocytes is consistent with various forms of viral infection, such as hepatitis. What is the probability that a normal adult will have 40 or more lymphocytes? Infectious Disease The...
What is the probability a normal adult will have 50 or more lymphocytes? Infectious Disease The differential is a standard measurement made during a blood test. It consists of classifying white blood...
What is the appropriate procedure to test for a significant difference in means between the two groups? Nutrition The mean 1 sd of ln [calcium intake (mg)] among 25 females, 12 to 14 years of age,...