One of the most innovative advances in online fundraising during the past decade has been the rise of crowd-funding websites. While features differ from site to site, crowd-funding websites give...
As the author is creating this exercise, a weather reporter stated that there is a 20% chance of rain tomorrow. What is the probability of no rain tomorrow?
When making a random guess for an answer to a multiple choice question on an SAT test, the possible answers are a, b, c, d, e, so there is 1 chance in 5 of being correct.
A random sample of 500 customers is asked to comment on the take-out service at The Chicken Hut. Of the 500 customers surveyed, 400 said it was excellent, 32 thought it was fair, and the remaining...
Out of a sample of 200 students, 75 indicated that they preferred chocolate ice cream to vanilla ice cream. a. Estimate the value of the population proportion of those who preferred chocolate ice...
Solve the ODE by integration or by remembering a differentiation formula. y' = cosh 5.13x
Sam Simone is the manager of a family-run pet store. He is deciding whether to open an hour later on Sundays. From past sales on Sundays he has determined that the probability of zero sales during...
Every year, Fortune magazine lists the 100 best companies to work for, based on criteria such as pay, benefits, days off, and diversity. In 2018, the top three were Sales Force, Wegmans Food Markets,...
If Aaron tunes into his favorite radio station at a randomly selected time, there is a 0.20 probability that a commercial will be playing. a. Interpret this probability as a long-run relative...
At a particular college, 78% of all students are receiving some kind of financial aid. The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving...
Brunswick Trucking has signed a five-year lease with Ford Credit Canada Ltd. on a new truck. Lease payments of $1900 are made at the beginning of each month. To purchase the truck, Brunswick Trucking...
An experiment that involves learning in animals requires placing white mice and rabbits into separate, controlled environments: environment I and environment II. The maximum amount of time available...
For each shaded region in Problem, (a) Form the integral that represents the area of the shaded region and (b) Find the area of the region. y = x3+1 2 x = 1 -2 y = -x 1 2.
In Problem, equations are given whose graphs enclose a region. In each problem, find the area of the region. y = x 2 ; y = 4x - x 2
Ships A and B leave port together. For the next two hours, ship A travels at 20 mph in a direction 30 west of north while the ship B travels 20 east of north at 25 mph. a. What is the distance...
A normal population has a mean of 20.0 and a standard deviation of 4.0. a. Compute the z value associated with 25.0. b. What proportion of the population is between 20.0 and 25.0? c. What proportion...
Using simple moving averages and the following time series data, respond to each of the items. a. G raph the time series data. What do you observe? b. Compute all possible forecasts using a...
Find the limit or show that it does not exist. do lim (V4x2 + 3x + 2x) X -00
Identify the curve by finding a Cartesian equation for the curve. r = 4 sec
(a) Express the triple integral E f(x, y, z) dV as an iterated integral in cylindrical coordinates for the given function f and solid region E. (b) Evaluate the iterated integral. f(x, y, z) = x 2 +...
Let X be the winnings of a gambler. Let p(i) = P(X = i) and suppose that Compute the conditional probability that the gambler wins i , i = 1, 2, 3, given that he wins a positive amount. 1/3: p(1) %3...
According to Green Car Reports, 4.4% of cars sold in California in 2017 were hybrid cars. Suppose in a random sample of 500 recently sold cars in California 18 were hybrid. a. Write the null and...
Rhonda deposits $5,600 in a savings account that pays 1% interest, compounded semi-annually. Round to the nearest cent. a. How much interest does the account earn in the first 6 months? b. What is...
A girl has an age of x years. Her grandfather is aged y years. Write an expression for: a. Their combined age. b. The difference between their ages. c. The grandfathers age 10 years ago. d. The girls...
a. This cuboid has volume 768 cm 3 and the edges marked a are equal in length. Calculate the value of a. b. In another cuboid of length 12cm and volume 768 cm 3 , the width and height are not equal....
A circle, C, has equation x 2 + y 2 16x 36 = 0. a. Find the coordinates of the centre of the circle. b. Find the radius of the circle. c. Find the coordinates of the points where the circle meets...
What is the conditional probability that the man will be affected given that the woman is affected? How does this value compare with the prevalence in Table 3.5? Why should it be the same (or...
Assuming there are 1000 people 65+ years of age in the community, what is the expected number of cases of Alzheimers disease in the community? Suppose a study of Alzheimers disease is proposed in a...
Assume that the dominant, recessive, and sex-linked modes of inheritance follow the probability laws given in Problems 3.32, 3.37, and 3.40 and that, without prior knowledge about the family in...
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...
Answer Problem 6.67 for performance IQ? We have previously described Data Set LEAD.DAT (at www.cengagebrain.com), in which children were classified according to blood-lead level in 1972 and 1973 by...
Compare the percentage of Caucasian and African American women who are overweight. Report a two-tailed p-value?
Answer the question in Problem 11.64 for bone density at the femoral neck? Data from 11.64 Use regression analysis to relate the number of pack-years smoked to the bone density of the lumbar spine....
Repeat the analyses in Problem 14.39, but account for covariate differences between groups?
Find the mean and standard deviation of the household debt (DEBT) of the respondents in the 2013 survey. If we assume that debt is not bell shaped describe what the mean and standard deviation tell...
What is the relationship between your answers to Problems 6.12 and 6.13? Refer to the data in Table 2.13. Regard this hospital as typical of Pennsylvania hospitals. Table 2.13: Hospital-stay data
Refer to Exercise 9.36. Does your answer change if you discover that the times needed to mark a midterm test are not normally distributed?
The manager of a large shopping center in Buffalo is in the process of deciding on the type of snow clearing service to hire for his parking lot. Two services are available. The White Christmas...
Provide a 95% CI for the mean change in heart rate after using the treadmill for 5 minutes. The subject also recorded his heart rate at baseline and 5 minutes after starting treadmill exercise (at a...
What nonparametric test can be used to determine whether a significant change in periodontal status has occurred over time? Suppose patients are graded on the degree of change in periodontal status...
Use mixed effects methods to compare the mean change in TBUT immediately post-instillation against baseline according to participant (1, 2, . . . , 14) and nonblink time period (3 sec vs. 6 sec vs....
A sample of heights (in inches) of 20 female statistics students is as follows: 67, 64, 67, 65, 64, 65, 67, 64, 65, 60, 67, 67, 72, 65, 70, 63, 67, 65, 67, 70 a. Find the median height. b. Find the...
The bivariate distribution of X and Y is described here. a. Find the marginal probability distribution of X. b. Find the marginal probability distribution of Y . c. Compute the mean and variance of...
a. Describe the relevant long-run proportion of interest in words. b. What statistical term is given to the long-run proportion you described in (a)? c. What value does the chance model assert for...
For the following time series, compute the seasonal (daily) indexes. The regression line is yÌ = 16.8 + .366t (t = 1, 2, . . . , 20) Week Day 2 3 Monday Tuesday Wednesday Thursday Friday 12 11...
A radio station that currently directs its programming toward middle age listeners is contemplating switching to rock-and-roll music. After analyzing advertising revenues and operating costs, the...
Consider the hospital emergency room data given below. Use Bayes theorem to calculate the probability that a person visits hospital 4 given they are LWBS. Hospital Total 5640 Total 6991 4329 22,252...
Consider the hospital emergency room data given below. Let A denote the event that a visit is to hospital 4, and let B denote the event that a visit results in LWBS (at any hospital). Determine the...
A psychology study (Rutchick, Slepian, and Ferris, 2010) investigated whether using a red pen causes people to assign lower scores than using a blue pen. A group of 128 students in an introductory...
In a survey of introductory statistics students, an instructor asked her students to report how many Facebook friends they had. Suppose that the intent is to study whether there is an association...
Determine whether the distribution represents a probability distribution. If it does not, state why. 16 9. 4 9. | 1 P(X)
A researcher wishes to determine the number of cups of coffee a customer drinks with an evening meal at a restaurant. Find the mean, variance, and standard deviation for the distribution. 1 2 3 2...
What are the IQ scores associated with the middle 61% of scores?
Assume systolic blood pressure is normally distributed, with a mean of 124 and a standard deviation of 16. Saritas systolic blood pressure, as a percentile rank, is 20. What is her systolic blood...
What is the percentile rank for a z score of 1.57?
What percentage of scores in a normal distribution fall at or below a z score of 2.57?
What percentage of cases in a normal distribution fall at or below a z score of 2.34?
Jong-Il was feeling depressed and anxious. His therapist gave him a depression test (M =10, s = 3, higher scores mean more depression) and an anxiety inventory (M = 80, s = 25, higher scores mean...
Svens score on an IQ test, expressed as a z score, is .38. What was his score?
Paolo, a kindergarten student was given a pack of colored construction paper with 10 pages each of red, orange, yellow, green, blue, indigo, violet, black, and white. His favorite color is green....
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...
An article in Computers & Electrical Engineering [Parallel Simulation of Cellular Neural Networks (1996, Vol. 22, pp. 6184)] considered the speedup of cellular neural networks (CNN) for a parallel...
HSD stands for ____.
Supercavitation is a propulsion technology for undersea vehicles that can greatly increase their speed. It occurs above approximately 50 meters per second when pressure drops sufficiently to allow...
Find P(z < 2.3 or z > 1.2).
Since 1975 the average fuel efficiency of U.S. cars and light trucks (SUVs) has increased from 13.5 to 25.8 mpg, an increase of over 90%! A random sample of 40 cars from a large community got a mean...
You are watching two items posted for sale on eBay and bid $30 for the first and $20 for the second item. You estimate that you are going to win the first bid with probability 0.1 and the second bid...
Find the 95% confidence interval of the difference in the distance that day students travel to school and the distance evening students travel to school. Two random samples of 40 students are taken,...
Given this matrix, how many degrees of freedom are there for this chi-square test of independence?
Given the information below, calculate chi-square: Observed Frequencies Outcome A Outcome B Group I Group II 18 10
Level of anxiety before a test, as measured 04 on a scale marked 0 = none, 1 = slight, 2 = moderate, 3 = considerable, and 4 = extreme (a) Whether the variable is measured at the nominal, ordinal,...
Clinicians at a nursing home facility want to see if giving residents a plant to tend to will help lower depression. To test this idea, the residents are randomly assigned to one of three groups:...
Find the standard matrix of the orthogonal projection onto the subspace W. Then use this matrix to find the orthogonal projection of v onto W. W = span| -2 3 -1
Terminology If a numerical measure describes an aspect of a sample, is it a statistic or a parameter?
A cognitive psychologist wanted to investigate the stage of moral development reached by college students. She believed that people progressed, in order, through six stages of moral reasoning, from...
a. Find the range for the data in Exercise 3.41. b. Which is a better measure of variability to report, the range or the interquartile range? Why? Data from problem exercise 3.41 Find the median and...
A consumer group is planning to do 2 twosample t tests. In Test 1, they are going to put together a random sample of items at a jewelry store and compare the prices to a random sample of items at a...
The average gasoline price per gallon (in cities) and the cost of a barrel of oil are shown below for a random selection of weeks in 2015. Find the cost of gasoline when oil is $60 a barrel. For each...
People whose blood type is O-negative are universal donorsanyone can receive a blood transfusion of O-negative blood. In the U.S., 7.2% of the people have O-negative blood. A blood donor clinic wants...
Baseball teams A and B face each other in the World Series. For each game, the probability that A wins the game is p, independent of other games. Find the expected length of the series.
In Newman (2005), the population of U.S. cities larger than 40,000 is modeled with a Pareto distribution with a = 2.30. Find the probability that a random citys population is greater than k = 3, 4,...
Calculate the value of the z test for each of the following situations: a. hyp = 100; = 16; n = 25; X = 94 b. hyp = 100; = 15; n = 9; X = 108 c. hyp = 150; = 20; n = 81; X = 130 d. hyp = 150; ...
A random experiment takes r possible values, with respective probabilities p 1 , . . . ,p r . Suppose the experiment is repeated N times, where N has a Poisson distribution with parameter . For k =...
A new post-surgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven others (the controls) receive the standard treatment. The recovery...
The density of a random variable X is given by Let Y = e X . (a) Find the density function of Y (b) Find E[Y] two ways: (i) Using the density of Y and (ii) Using the density of X. 3x2, for 0 < r < 1...
Let A = UV, where U and V are independent and uniformly distributed on (0,1). (a) Find the density of A. (b) Find E[A] two ways: (i) Using the density of A and (ii) Not using the density of A.
Let X and Y have joint density f(x, y) = x + y, 0 < x < 1, 0 < y < 1. Find E[X|Y = y].
Let X and Y have joint density function 0,0 < y < e 1. " style="" class="fr-fic fr-dib"> (a) Find and describe the conditional distribution of X given Y = y. (b) Find E[X|Y = y] and E[X|Y]. (c) Find...
The population is adults between the ages of 18 and 22. A sample of 100 students is collected from a local university, and each student at the university had an equal chance of being selected for the...
A fitness center weighed 53 male athletes and then measured the weight that they were able to lift. The correlation was found to be r = 0.75. Can you interpret this correlation without knowing...
A customized milling operation uses the equation $200 plus $150 per hour to give price estimates to customers. If it pays a fixed fee to ship these orders, how should it change this equation if the...
Find a basis of solutions by the Frobenius method. Try to identify the series as expansions of known functions. Show the details of your work. xy" + y = 0
Introductory statistics students fill out a survey on the first day of class. One of the questions asked is How many hours of exercise do you typically get each week? Responses for a sample of 50...
Determine whether it is appropriate to use the normal distribution to estimate the p-value. If it is appropriate, use the normal distribution and the given sample results to complete the test of the...
At Bigbrain University, the typical grade distribution is A, 15%; B, 25%; C, 45%; D, 10%; F, 5%. The grades given by two professors are shown here. For each one (separately), test the null hypothesis...
How many different samples of 4 objects can we draw from a lot of 50?
In a survey of college students, it was found that 356 owned an iPad. 293 owned a laptop. 285 owned a gaming system. 193 owned an iPad and a laptop. 200 owned an iPad and a gaming system. 139 owned a...
Determine which, if any, of the three statements are equivalent. (a) It is not true that the test is today or the concert is tonight. (b) The test is not today and the concert is not tonight. (c) If...
We show lattice multiplications. (a) Determine the numbers being multiplied. (b) Determine the product. 8. 00