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Population mean   In different condition the population mean may results in different way Let us consider two different condition in which population mean have to test. One is when population variance is known and other is when population variance is unknown. When population variance is known, Let Null hypothesis is equal to or less than 20 Alternative hypothesis is greater than 20 The known significance level is .05, Hence, type one error should not exceed .05. We also know that probability of type one error will highest when meu is in breakpoint, Another two test should proceed, One tailed test two tailed test Let us consider, Null hypothesis is equal to 20 Alternative hypothesis not equal to 20 The significance level is equal to .05 One tailed test implies in that situation when critical region place under the one tail, specially right tail shaded area. In contrast with two tail test the critical region places under both tail of the distribution....

Hypothesis testing Hypothesis testing is a testing of decision predicted or a statement in order to accept or reject of any statement to make an authentic decision. In any of the hypothesis testing two error should be taken into under consideration. Type one error Type two error In all types of hypothesis testing type one error is more serious than type two error. Hence, decision maker in any scientific investigation tries to control type one error with more attention. The controlling of type one error is related with the significance level of the test at which the tests are ongoing. Let us set up hypothesis as Null hypothesis = 50 Alternative hypothesis not equal to 50 The sample mean is x The condition of rejecting of Null hypothesis is only when sample mean is greater than 53 or less than 47. But, if the sample mean place between 47 to 53 that is closer to 50, is not strong evidence of rejecting null hypothesis. A null hypothesis can be reject in significance...

Before explaining about Null Hypothesis, let us discuss about the conception of Hypothesis. Hypothesis Hypothesis is a statement about a population parameter or population distribution. Any statement that should be tested for discovering the authenticity in order to making a decision is Hypothesis. Any claim by a producer against his product is simply a hypothesis that should be tested by the customer that the claim is true or not in order to make a decision to purchase or not. Hypothesis testing Two set of hypothesis may found in a hypothesis testing. Null hypothesis and alternative hypothesis. The true statement from a pair of hypothesis is termed as Null hypothesis and other statement is alternative hypothesis. Hypothesis testing is used for making a decision to accept or reject any of the statement. Accepting or rejecting of statement is depends of the true evidence against the statement. Let consider  about any statement of any product stability claimed by pr...

Probability sampling method   There are available most important probability sampling method is given bellow, Simple random sampling Systematic sampling Stratified sampling Cluster sampling Simple random sampling When the population size is very small in this case simple random sampling is very effective.  it is a simplest method of sampling for small population. Simple random sampling method implies that each of the element of population have an equal chance of selecting as a sample. Just consider you are going to select n sample size from a population of N elements. If you do not consider any properties of the sample what you should select, then there have equal chance of each elements of the population of being selected. Systematic sampling Systematic sampling method is a method of sampling design that perform by selecting of sample or elements after a certain interval depending on a sampling ratio. The basic difference and advantage of systematic s...

Introduction of probability The conception of probability mathematics is emerged in real world due to uncertainty. In real life peoples found a great range of uncertainty ab out any outcome. The uncertainty exists in all of the field surrounding us. Uncertainty, exists in physics, mathematics, chemistry, economics, social science as well as in contest of cosmos. If we sure about any consequence of happening, it may not happen at all. That is uncertainty. The uncertainty of real world leads to emergence of probability mathematics. Probability Simply, probability means the chance of occuring of any consequence. If you toss a coin there have a two chance of happening of two consequence. Either, result of coin tossing may be head or tail. What should be happening of head in coin tossing. The probability of happening of head is half and probability of happening of tail is half. Some basic concepts of probability Experiment The term experiment is doing something and no need i...

Quantiles Quantiles is a most important measure of central tendency which is involved in the positional measure of non central position. Quartiles, deciles and percentiles are such types of quantiles that measures the non central position of the observed data.  Quartiles Quartiles divide the total data into four equal parts. In order to divide a bulk size of data into four equal parts there need three point. Three point equal distance from each other can equally divide any distribution into four equal parts. Deciles Deciles are such types of quantiles of central tendency that divides the total distribution of the data into ten equal parts. Percentiles Percentiles are the values that divide the distribution into hundred of equal parts.

Central tendency  The term central tendency is highest level of authenticity in mathematics, statistics, physics, chemistry, economics, even in all of the field of study and investigation. Hence, the conceptation of central tendency should clearly understand. The general understanding of central tendency is look the principle insight on the central core theme. The measurement of central value of something gives an inference about the complete and entire themes.  Just look at an example, If you know the mass of nucleus of the atom, you have known the entire mass of the atom. How the earth attracting some objects toward itself in what of the force there  need a measurement of attraction of the central point of the objects to the earths central point. The total income of households of Chicago is possible to measure in  billions of amount. Here, different people have different income. It is very hard to say about any specific peoples income. But, it is po...