All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Hire a Tutor
AI Study Help New

Search
Sign In
Register

study help
business
introduction to statistical investigations

Questions and Answers of Introduction To Statistical Investigations

Aresearcher investigating a new product for clearing up acne selects a random sample of 10 teenagers, gives them the facial product to use, and asks that they report back how many days it took for
The following is a list of Levels of Service Inventory (LSI) scores taken from a sample of 10 inmates on their first day of incarceration at a county correctional facility. The LSI is a measure of
Asample of 10 patients from a county forensic unit were tested for psychopathy using the Holden Psychological Screening Inventory (high scores indicating higher levels of psychopathy). Their scores
The IQs of all students at a certain prep school were obtained. The highest was 135, and the lowest was 105. The following IQs were identified as to their percentile:a. What is the range for the
The grade-point averages for the seven university students selected in the previous problem were computed. The data are as follows:For the GPAdistribution, calculatea. the mean.b. the range.c. the
A group of seven university students was randomly selected and asked to indicate the number of study hours each put in before taking a major exam. The data are as follows:For the distribution of
Despite the facts that the two groups of workers in problems 1 and 2 saved the same mean amount and that the ranges of amounts saved are identical, in what way do the two distributions still differ?
At Company Y, another group of eight blue-collar workers was selected and asked how much of each saved of their weekly pay. The following is the list of amounts saved: $20, $18, $3, $2, $1, $16, $15,
At Company X, a group of eight blue-collar workers was selected and asked how much of their weekly pay (in dollars) each put into their savings bank accounts. The following is the list of amounts
It makes little or no difference which measure of central tendency is used, since they all “average out” about the same anyway.
When skewed data are used, the median is the best index of central tendency.
The median of a given distribution is 20, the mode is 17, and the mean is 35. The distribution is skewed to the left.
If a distribution is perfectly symmetrical, it must have only one mode.
The median is always that point that is arithmetically exactly halfway between the highest and lowest scores in a distribution.
In a positively skewed distribution, the mean lies to the left of the median.
The mean is influenced more than the median by a few extreme scores at one end of the distribution.
When finding the median, it makes no difference whether one starts counting from the top or the bottom of the distribution of scores.
The mean number of years of marriage preceding divorce is 7. The median number of years is 6. Most divorces occur, however, either at 3 years of marriage or at 22 years.Which measure of central
The most frequently occurring score in any distribution defines which measure of central tendency?
If the distribution is skewed to the left, what is the appropriate measure of central tendency?
If the median is substantially higher than the mean, in which direction is the distribution skewed?
If the mean is substantially higher than the median, in which direction is the distribution skewed?
If a distribution is skewed to the left,a. which measure of central tendency yields the highest value?b. which yields the lowest?
If a distribution is skewed to the right,a. which measure of central tendency yields the highest value?b. which yields the lowest?
For the following distributions, estimate whether they are skewed, and if so, in which direction. = a. M = 50, Mdn b. M = = 110, Mdn c. M 50, Mo = 50. 100, Mo = 90. 450, Mdn 500, Mo = 550. -
The following is a list of the retirement ages for the workers in a certain production plant: 65, 61, 63, 62, 65, 62, 65, 64, 62.a. Find the mean, the median, and the mode.b. Which measure of central
Here is a set of scores: 100, 5, 12, 17, 12, 9, 3, 12.a. Find the mean, the median, and the mode.b. Which measure of central tendency is the most appropriate, and why?
Aweek later, the group of 13 counselees mentioned in problem 7, take the same test a second time. This time their scores were: 11, 11, 11, 11, 12, 14, 20, 10, 10, 9, 2, 8, 9.a. Find the mean.b. Find
Immediately following the coverage of an anger-reduction unit, a group of 13 young men, all counselees in an anger rehab program, were given a 20-item quiz on the material presented. Their scores,
Agroup of 10 elderly patients in a nursing home is asked how much time each spends watching TV. Their scores (in hours per week) are as follows: 40, 55, 50, 40, 10, 35, 40, 35, 50, 40. Find the mean,
Arandom sample of six inmates was selected from the state’s prison population, and they were given the OVP (Overt Violence Potential) test, with higher scores indicating a higher potential for
Find the percentage change for the following:a. 100 to 250b. 60 to 75c. 100 to 50d. 500 to 150
a. 10 is 20% of what?b. 500 is 80% of what?
a. 75 is what percent of 150?b. 8 is what percent of 50?
a. Find 15% of 60.b. Find 24% of 400.
Fatalities per million miles of driving are 5.1 for men and 5.9 for women. Be careful not to assume that this proves that men are better and safer drivers than are women.What else must be known to
Bullying is the repeated physical or psychological mistreatment by a peer who is physically or psychologically stronger than the victim. Dan Olweus cites evidence showing that the victims of bullying
Studies have shown that whereas armed citizens shoot the wrong person 2% of the time, police officers do so 11% of the time (Poe, 2001). Does this mean that police officers are more careless and less
In a study of over 14,000 high school students, reported in September 2000, it was found that teens, both boys and girls, who were members of sports teams were less apt to engage in a number of
The opening of a new Broadway musical in April of 2001, “The Producers,” led news accounts to rave that box-office advance sales set an all-time popularity record, with almost $3 million worth of
The heights of 2,848 students, ages 5–13, were recorded and it was found that at every grade level, the oldest students in the class were the shortest (Wake, Coghlan, &Hesketh, 2000). The
In 2006, it was said that senior citizens were spending twice as much on prescription drugs as they did eight years earlier. Does this mean that big, greedy drug companies were charging twice as much
With a nice four-day holiday weekend ahead, you’re cruising down the highway and listening to your favorite music station when suddenly you hear the National Safety Council’s warning that over
It was reported that at a certain university in the United States, only 50% of the student athletes in the major sports programs (Division 1 football and basketball) were graduating within the
Two separate research studies conducted in 1994 came up with the same finding, that men in the corporate world who had working wives earn less money than the men whose wives stayed home to care for
A research study reported a linkage between learning disabilities and crime. Data from the Brooklyn Family Court (1988) indicated that 40% of the juveniles who appeared in court were learning
Two major automakers, one in the United States and the other in Japan, proudly announce from Detroit that they will jointly produce a new car. The announcement further states (patriotically) that 75%
A marketing research study reported that a certain brand of dishwashing detergent was found by a test sample to be 35% more effective. What else should the consumer find out before buying the product?
A statewide analysis of speeding tickets found that state troopers in unmarked cars were giving out 37% more tickets over holiday weekends than were troopers working from cruisers that were clearly
A toothpaste company says that a large sample of individuals tested after using its brand of toothpaste had 27% fewer dental caries. Criticize the assumption that using the company’s toothpaste
An oil company grandly proclaims that its profits for the fourth quarter increased by 150% over those in the same period a year ago. On the basis of this statement, and assuming that you have the
Arecent TV ad tried to show the risks involved in not taking a certain antacid tablet daily.The actor, wearing the obligatory white coat and stethoscope, poured a beaker of “stomach acid” onto a
Acertain Swedish auto manufacturer claims that 90% of the cars it has built during the past 15 years are still being driven today. This is true, so say the ads, despite the fact that the roads in
During the crisis in Iraq, the number of Americans who died there was lower (for the same time period) than the number of Americans who died in the United States.Therefore, one can conclude that it
7.2 Let X and Y have twice differentiable densities f0 and g0, and f and gbe the respective densities of Z1 = X +pV and Z2 = Y +pV, where V is independent of X and Y and EV = 0, EV 2 = 1. If X Y and
7.1 Let f be the density of Z = X +pV, i.e., X is affected by an additive measurement error p V. Assume that X and V are independent, X has continuous symmetric density f0 and V has strongly unimodal
6.3 Let X1, . . . ,Xn be a sample from a population with distribution function F(x−), and F symmetric around 0. The -trimmed mean Tn(), defined in Example 3.2 is asymptotically normally
6.2 Let F be the family of densitieswhere f0 is a fixed density (but generally unknown) such thatand f0 has a bounded derivative in a neighborhood of 0.Consider the linear regression model Yi = x0 i
6.1 Let X1, . . . ,Xn have distribution function F(x−) where F is symmetric around 0. Let Tn be Huber’s M-estimator generated by the -function(3.16) with the boundary k. Then p n(Tn − ) has
5.4 Let x1, . . . , xn and 1, . . . , n be the same as in Problem 5.3 and i =(1995) and by Marden (1998). Chaudhuri (1996) considered the corresponding multivariate quantiles ni/1), i = 1,...,n.
5.3 Let x1, . . . , xn be distinct points in Rp. Consider the minimization ofwith respect to y 2 Rp, where 1, . . . , n are chosen positive weights. The solution of (5.31) is called the
5.2 Let T1 and T2 be two competing estimators of and L(·, ·) be a lossfunction. DenoteTable 5.4 Powers of two-sample Hotelling T2 test (H), two-sample Wilcoxon test (W) and two-sample N−distance
5.1 X is spherically symmetric about if and only if
4.9 Let us consider an R-estimator minimizing the rank dispersion (4.48)If we set = then this R-estimator coincides with the slope components of regression -quantile b () solving (4.54), see
4.7 The Wilcoxon-type test of hypothesis H : (2) = 0 in the model(see (4.69), X(1) is n × p and X(2) is n × q), based on the regression rank scores, is based on the following criterion. Assume that
4.6 Let b n() be a solution of the minimization (4.54) (the regression -quantile, thenwhere is the function from problem 4.4 (Ruppert and Carroll (1980)). n n xva (Y-x (a))0a.s. as n i=1
4.5 Let ri = Yi−x0 ib 0, i = 1, . . . , n be the residuals with respect to estimator b0 of , and let n be the solution of the minimizationwhere is the criterion function of an -regression quantile
4.3 Another possible characteristic of performance of L-estimators in the linear model is the largest integer m such that, for any set M N ={1, . . . , n} of size m, inf iEN-M|xb| ||b||=1 ien xb 2
3.7 Let X1, . . . ,Xn be a sample from the Cauchy distribution C(, ) with the density f(x)= 1 + (x - ) Then the distribution of X, is again C(,0)
3.9 Consider the equationwhere C is the Cauchy likelihood function (3.18). Denote Kn as the number of its roots. If X1, . . . ,Xn are independent, identically distributed with the Cauchy C(0, 1)
3.8 Let be a random angle with the uniform distribution on the unit circle. Then tg X has the Cauchy distribution C(0, 1). X, X,
3.6 Tukey (1960) proposed the model of the normal distribution with variance 1 contaminated by the normal distribution with variance 2 > 1, i.e., that of the distribution function F of the
3.3 The symmetrized -interquantile range (0 S1/4 coincides with MAD. Calculate the influence function of ˜ Sa. where Sa(F) Sa(F) = (1 - a) - F (a) F(x) {F(x)+1-F [2F()]} for F continuous
3.2 The -interquantile range (0 The influence function of S equals Sa F-(1-a) - F-1 (a).
3.1 Let X1, . . . ,Xn be a sample from the distribution with the density 1 if x f(x) = 32rif x>
2.5 Let Tn(X1, . . . ,Xn) be a random sample from a population with distribution function F(x − ). Compute the breakdown point ofThis estimator is called the midrange (see the next chapter). Tn =
2.4 Let Tn(X1, . . . ,Xn) be a translation equivariant estimator of , nondecreasing in each argument Xi, i = 1, . . . , n. Then, under the conditions of Problem 2.2,Illustrate it on the sample
2.3 Let X1, . . . ,Xn be a random sample from a population with distribution function F(x − ), where F is symmetric, absolutely continuous, 0 , nondecreasing in each argument Xi, i = 1, . . . , n.
2.2 Characterize distributions satisfyingfor any fixed c 2 R. Show that this class contains distributions of Type 1 and Type 2. lim -In(1- F(a+c)) -In(1 - F(a)) 1
1.11 Compute the Wasserstein-Kantorovich distances andfor the exponential distribution and the uniform distribution (as in Example 1.6). dW (F,G)
1.8 Verify 2dy (P,Q)=xdP - dQ|.
1.7 Bhattacharyya distance: Let p, q be the densities of probability distributions P, Q with respect to measure. Then dB(P,Q) is defined as(Bhattacharyya (1943)). Furthermore, for a comparison dB
1.6 Let P be the exponential distribution and let Q be the uniform distribution(see Example 1.6) Thenhence dX2 (R(0, 1), exp) 0.350402. Furthermore,hence d2(exp,R(0, 1)) 0.168091 1), (db) exp da
1.5 X2-distance: Let p, q be the densities of probability distributions P, Q with respect to measure μ (μ can be a countable measure). Then dX2 (P,Q)is defined asThen 02 (P,Q) 1 and d2 is
1.4 Let (X1, . . . ,Xn) and (Y1, . . . , Yn) be two independent random samples from distribution functions F, G such that(Mallows (1972)). 2% xdF(x) = 2% ydG(y) = 0.
1.3 Show that dp(F,G) dw (F,G) (Dobrushin (1970)).
1.2 Wasserstein-Kantorovich distance of distribution functions F, G of random variables X, Y :jointly distributed X and Y with respective marginals F and G. L-distance on F = {F: |x|dF(x)
1.1 Let Q be the binomial distribution with parameters n, p and let P be the Poisson distribution with parameter = np, thenSee Barbour and Hall (1984), Csiszár (1967), Harremoës and Ruzankin
Let T be a statistical functional, Fréchet differentiable in P, and assume that the empirical probability distribution Pn of the random sample(X1, . . . ,Xn) satisfies the condition (1.16) as n !
3.74. In a study of graduate students who took the Graduate Record Exam (GRE), the Educational Testing Service reported that for the quantitative exam, U.S. citizens had a mean of 529 and standard
3.73. The 2004 GSS asked whether having sex before marriage is (always wrong, almost always wrong, wrong only sometimes, not wrong at all). The response counts in these four categories were (238, 79,
3.72. In Canada, based on the 2001 census, for the categories (Catholic, Protestant, Other Christian, Muslim, Jewish, None, Other) for religious affil- iation, the relative frequencies were (42 %, 28
3.71. Answer true or false to the following: (a) The mean, median, and mode can never all be the same. (b) The mean is always one of the data points. (e) The median is the same as the second quartile
3.70. To measure variability, why is (a) The standard deviations usually preferred over the range? (b) The IQR sometimes preferred to s?
3.69. To measure center, why is the (a) median sometimes preferred over the mean? (b) Mean sometimes preferred over the median? In each case, give an example to illustrate your answer.
3.68. Give an example of a variable having a distribution that you expect to be (a) approximately symmetric, (b) skewed to the right,
3.67. Give an example of a variable for which the mode applies, but not the mean or median.
3.66. According to a report from the U.S. National Cen- ter for Health Statistics, for males age 25-34 years, 2% of their heights are 64 inches or less, 8% are 66 inches or less, 27% are 68 inches or
3.64. A U.S. Federal Reserve study in 2000 indi- cated that for those families with annual incomes above $100,000, their median net worth was about $500,000 both in 1995 and in 1998, but their mean
3.63. In 2001, the U.S. Federal Reserve sampled about 4000 households to estimate overall net worth of a family. The Reserve reported the summaries. $86,100 and $395,500. One of these was the mean,

Showing 400 - 500 of 1982

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Last

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Secure Payment

Download Our App

© 2024 SolutionInn. All Rights Reserved