A method of selecting a sample (random sample) from a statistical population in such a way that every possible sample that could be selected has a predetermined probability of being selected.

Rejecting the null hypothesis when it is in fact true is called a Type I error.

An F-test is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test.
The two-tailed version tests against the alternative that the variances are not equal.
The one-tailed version only tests in one direction, that is the variance from the first population is either greater than or less than (but not both) the second population variance. The choice is determined by the problem.

Ibid meaning "in the same place", commonly used in an endnote, footnote, bibliography citation, or scholarly reference to refer to the source cited in the preceding note or list item. This is similar to īdem, literally meaning "the same", abbreviated id., which is commonly used in legal citation.
“Et al.” is a scholarly abbreviation of the Latin phrase et alia, which means “and others.” It is commonly used when you don't want to name all the people or things in a list, and works in roughly the same way as “etc.”

For a given sample, the 99% confidence interval would be wider than the 95% confidence interval, because it allows one to be more confident that the unknown population parameter is contained within the interval.

For approximately equal average values, the one with a higher standard deviation is more scattered
For approximately equal standard deviation values, the one with a lower average is more scattered
If both the averages and standard deviations differ much between the series, we can compare scattering using the coefficient of variation

For typical analysis, using the standard α = 0.05 cutoff, the null hypothesis is rejected when p < .05 and not rejected when p > .05. The p-value does not, in itself, support reasoning about the probabilities of hypotheses but is only a tool for deciding whether to reject the null hypothesis.

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals made in the results of every single equation

There are a total 7 possibilities,because a month can start with any of the 7 days of the week .But there are only 3 possibilities of getting monday 5 times , if the month either starts with saturday or sunday or monday. So the required probability is 3/7.

Given that out of two children one is definitely girl.So the total possibilities are , {girl,boy} ,{girl,girl}
So the probability that another child is also a girl is =½.

Count up the number of factors of 5 and the number of factors of 2 in 20!. Since we get a zero for every pair of factors 5x2, then the minimum of these will answer your question. More simply, 5 happens less often as a factor (since it's bigger than 2), so we need only count up the number of 5's. In particular, there's one each in 5,10,15,20, so there are 4 zeroes at the end.

If the value of N is 4 then choosing at least 15 samples from the collection guarantees that u have 6 samples of the same type of mineral, because in worst case choose 4 from each collection then we have 4 samples of the same type of mineral and now siderite is finished and we have to select from remaining two samples .Now select 2 from 1 sample and 1 from other in worst case. Now we have selected 15 items out of which 6 are definitely from the same type of mineral.

We use the concept of Euler to find function. It is used to give the no. of numbers which are less than and relatively prime to n and is represented as, Q(n).
So, ATQ,
n = p = q = 110179 ---(1)
and Q(n) = (p-1)(q-1) = 109480 ---(2)
Now let’s solve (2),
pq - p - q + 1 = 109480
Let put value of pq from (1),
110179 - p - q + 1 = 109480
110180 - 109480 = p + q
Therefore p+q = 700

10² × 4³ plates without vowel O + 9² × (5³ − 4³ ) plates with vowel O but without 0. This gives 6400 + 4941 = 11341.

Consider the position of the alphabets A is 1, B is 2, C is 3 and so on then
PROJECTION word gets the following numbers
P is 16, R is 18, O is15, T is 20, E is 5, C is 3, T is 20, I is 9, O is 15, N is 14
The letters O,E,C,I,O are in the odd positions 15,5,3 and 15 respectively
After arranging that letter alphabetical order ,C,E,I,O,O
Now substitute the above letters by Z,Y,X and so on then X will come in place of I.

According to the question rank of gopal from top is 7+4=11. Hence rank of gopal from bottom is 35-11+1 =25.

P and Q are brothers. Q is son of S and T. S is daughter of U and B is son of U,means B is brother of S.Hence son of S will be nephew of B.Hence P is nephew of B.