Given the test scores of two random samples of men and women, does one group differ from the other?

Given the model and realizations ( samples ) of the random vector, the task is to estimate both the mixing matrix and the sources.

Given that the ruins of the gas chambers at Birkenau have been washed by a column of water at least 35m in height based on climatological records since 1945, Markiewicz and his team were not optimistic at being able to detect cyanides so many years later ; nevertheless, having the legal permission to obtain samples, they collected some from areas as sheltered from the elements as possible.

Most methods of lipid extraction and isolation from biological samples exploit the high solubility of hydrocarbon chains in organic solvents. Given the diversity in lipid classes, it is not possible to accommodate all classes with a common extraction method.

Given the absolute magnitude, for objects within our galaxy you can also calculate the apparent magnitude from any distance ( in parsecs ):

Given the absolute magnitude, you can also compute apparent magnitude from its parallax:

Given any element x of X, there is a function f < sup > x </ sup >, or f ( x ,·), from Y to Z, given by f < sup > x </ sup >( y ) := f ( x, y ).

Given BASIC's straightforward nature, it was a simple matter to type in the code from the magazine and execute the program.

Love and Erlandson continued to pursue with the band, and released the single " Be A Man "— an outtake from the Celebrity Skin sessions — for the soundtrack of the Oliver Stone film Any Given Sunday ( 1999 ).

Given r, the rate of rotation is easy to infer from the constant angular momentum L, so a 2D solution can be easily reconstructed from a 1D solution of this equation.

Given two manifolds M and N, a bijective map f from M to N is called a diffeomorphism if both

Given the similarities between the rep proteins of the alphasatellites and the nanoviruses, it is likely that the alphasatellites evolved from the nanoviruses.

) Given a smooth Φ < sup > t </ sup >, an autonomous vector field can be derived from it.

Given that the vast majority of all emeralds are treated as described above, and the fact that two stones that appear visually similar may actually be quite far apart in treatment level and therefore in value, a consumer considering a purchase of an expensive emerald is well advised to insist upon a treatment report from a reputable gemological laboratory.

Given that genes are universal to living organisms, genetics can be applied to the study of all living systems, from viruses and bacteria, through plants and domestic animals, to humans ( as in medical genetics ).

Given two groups (< var > G </ var >, *) and (< var > H </ var >, ), a group isomorphism from (< var > G </ var >, *) to (< var > H </ var >, ) is a bijective group homomorphism from < var > G </ var > to < var > H </ var >.

Given a groupoid in the category-theoretic sense, let G be the disjoint union of all of the sets G ( x, y ) ( i. e. the sets of morphisms from x to y ).

Given a groupoid G, the vertex groups or isotropy groups or object groups in G are the subsets of the form G ( x, x ), where x is any object of G. It follows easily from the axioms above that these are indeed groups, as every pair of elements is composable and inverses are in the same vertex group.

: Given a point ( in terms of its coordinates ) and the direction ( azimuth ) and distance from that point to a second point, determine ( the coordinates of ) that second point.

On poverty, Hoover said that " Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God, be in sight of the day when poverty will be banished from this nation ", and promised, " We in America today are nearer to the final triumph over poverty than ever before in the history of any land ," but within months, the Stock Market Crash of 1929 occurred, and the world's economy spiraled downward into the Great Depression.

Given the Greek fleet's unpreparedness resulting from the premature outbreak of the war, such an early Ottoman attack might well have been able to achieve a crucial victory.

Given MLB's refusal to consider expansion, Kirksey, Cullinan, Smith, and Hofheinz joined forces with would-be owners from other cities and announced the formation of a new league to compete with the established National and American Leagues.

Given the opportunity to get away from the Sultan and visit new lands, he readily accepted.

Given earlier debates by Christian authors about the existence of Jesus, e. g. in Justin Martyr's 2nd century Dialogue with Trypho, it would have been expected that the passage from Josephus would have been used as a component of the arguments.

Given significant distance from the magnetic poles, one can figure which hand is which using a magnetic compass and the sun.

Given printing practices at the time ( which included type-setting from dictation ), no two editions turned out to be identical, and it is relatively rare to find even two copies that are exactly the same.

Given a year to complete the work, Gibson undertook the actual writing out of " blind animal terror " at the obligation to write an entire novel – a feat which he felt he was " four or five years away from ".

) Given the exclusionary and ancestral conception of citizenship held by Greek city-states, a relatively large portion of the population took part in the government of Athens and of other radical democracies like it.

Given the rugged terrain of Ngazidja and Nzwani, and the dedication of extensive tracts to agriculture on all three islands, population pressures on Comoros are becoming increasingly critical.

Given the small population of the region ( compared with the Central Canadian provinces or the New England states ), the regional economy is a net exporter of natural resources, manufactured goods, and services.

Given the geographic diversity of the various sub-regions within the Maritimes, policies to centralize the population and economy were not initially successful, thus Maritime factories closed while those in Ontario and Quebec prospered.

We have seen a few cavities of the appropriate size and shape for ivory-bills, but these can be old, or exceptionally large Pileated Woodpecker cavities, or mammal-enlarged Pileated Woodpecker cavities .… Given the results, it is unlikely a population of any meaningful size of Ivory-billed Woodpeckers exists in south Florida.

Given enough time and repeated exposure to the antibiotic, a population of antibiotic-resistant bacteria will emerge.

" Given, a certain population, with various needs and powers of production, in possession of certain lands and other sources of material: required, the mode of employing their labour which will maximize the utility of their produce.

Given population growth rates, the figure in 2010 might be half again higher.

Given that coconuts are ideally suited for ocean dispersal, it seems possible that individuals from one population could have floated to the other.

Given the rapidity with which its last population was eliminated, it is likely that aboriginal hunting caused its extinction over the rest of its original range ( aboriginal peoples apparently never inhabited the Commander Islands ).

Given the growth of the town of Oxnard, in the spring of 1898, a railroad station was built to service the plant, which attracted a population of Chinese, Japanese, and Mexican laborers and enough commerce to merit the designation of a town.

Given the borough's small size, as well as the county's small population, the presence of business and government remain limited.

Dr. Tennison states: " Given the account of Elliot Paul, and given that Lead Belly witnessed boogie-woogie in 1899 in the Arklatex ; and given the North to South migration of the Thomas family ; and given the Texas & Pacific headquarters in Marshall in the early 1870s ; and given that Harrison County had the largest slave population in the state of Texas ; and given the fact that the best-documented and largest-scale turpentine camps in Texas did not occur until after 1900 in Southeast Texas, it is most probable that boogie-woogie spread from Northeast to Southeast Texas, rather than from Southeast to Northeast Texas, or by having developed diffusely with an even density over all of the Piney Woods of East Texas.

Given the extensive linguistic, religious and ethnic diversity of the Indian population, nationalism in India in general does not fall within the purview of a solitary variant of nationalism.

Given their limited range, they can only meet the needs of 90 percent of the population.

Given the morphological distinctness of the Cape Verde birds and the fact that the Cape Verde population was isolated from other populations of Red Kites, it cannot be conclusively resolved at this time whether the Cape Verde population was not a distinct subspecies ( as M. migrans fasciicauda ) or even species that frequently absorbed stragglers from the migrating European populations into its gene pool.

Given the current human population and birth-rate, this equals five per day or 1800 per year.

Given that average size of a peasant family was 5, land reforms program brought freedom to approximately 9 million people, or 40 % of Iran's population.

Given the small number of NAION events with PDE5 use ( less than 1 in 1 million ), the large number of users of PDE5 inhibitors ( millions ) and the fact that this event occurs in a similar population to those who do not take these medicines, the FDA concluded that they were not able to draw a cause and effect relationship, given these patients underlying vascular risk factors or anatomical defects.

Given the predominantly French-speaking population, only CBC, the English-language television service funded by the government of Canada, is available over the air throughout the province.

Given its population, the West Island is of similar same size as Windsor, Kitchener, Longueuil, Saskatoon, Burnaby or Regina.

Given a sufficiently large sample size, a statistical comparison will always show a significant difference unless the population effect size is exactly zero.