A Business Encyclopedia

Sampling Distribution of the Difference Between Two Means

Definition: The Sampling Distribution of the Difference between Two Means shows the distribution of means of two samples drawn from the two independent populations, such that the difference between the population means can possibly be evaluated by the difference between the sample means.

Let say, there are two populations, first of size N1, with mean ?1, and standard deviation σ1 and the second of size N2, with mean ?2, and standard deviation σ2. The two independent random samples are drawn, one from the population of size N1 and the other from the population of size N2. Suppose 1 and 2 are the two sample means, then we can estimate the possible difference between the population means, Viz. ?1 -?2 by the difference of sample means 1 – X͞2.

The following are the main properties of the sampling distribution of the difference between two means (1 – X͞2):

  • When the samples are selected randomly from the two independent populations, then the mean of the sampling distribution of the difference between the two means, i.e. 1 – X͞2, denoted by? X͞1 – X͞2 is equal to the difference between the Population Means. Symbolically,
    difference between two means-1
  • The standard deviation of sampling distribution of differences between two means, i.e. 1 – X͞2 is also called as the standard error of X͞1 – X͞2 and is denoted by:difference between two means-2
    Since, 1 and X͞2 are the independent random variables, so the variance of their difference is equal to the sum of their variance.
  • If 1 and X͞2 are the means of two samples drawn from two large and independent populations the sampling distribution of the difference between two means will be normal.

Note: It is to be noted that when the sampling is done without the replacement, and the population is finite, then the following formula is used to calculate the standard error:

difference between two means-3

Leave a Reply

Your email address will not be published. Required fields are marked *


Related pages

what is a semantic differential scaledivestment strategyliability in hindimarginal product of labor definitionadams equity theory of motivationwhat are the advantages of laissez faire leadershipdelphi method forecastingwhat is operant conditioning theorygraph of perfectly elastic demandpsychological factors influencing consumer behaviourdefinition of hybridswhat is the definition of hire purchasepost office tax saving schemesgive an example of ethnocentrismexample of fmcg productsdefine delegativeethnocentric meaningmeaning of subordinatesivan parlorsubstitution method definition mathdisinvestment definitiondefine total utilitycyclical unemployment definition economicsgeocentric pricingcyclical unemploymendefine itemizedordinal approach to consumer equilibriumchannel member definitionlearned needs theory of motivationexamples of oligopoly markettall organisational structure advantages and disadvantageshrm activitiespersuasion tagalogmanagerial grid modelcheque defineexplain demand forecastingsfa salesdefinition of equipmentsdefine censuswhat does autocratic meanjane moutonteleological systemsdefinition geocentriclinear programming maximizationimportance of bin cardnominal scales definitionan indifference curve showsequi marginal utility definitiontransactional theory definitiondefine speculatorkarizma meaningblack scholes d1 d2job evaluation factor comparisonpolycentric orientation definitionfive forces of competition modelsocial loafingencirclement strategydefine retained profitwhat does it mean to divestmeaning of holisticallydefine asset turnoverdelphi technique examplesconditioning pavlovemployees epfprofitability index formulareward power and coercive powerautocratic leadership meaningvertical horizontal and multichannel marketing systemsmax weber principles of managementspeculators definitionjoseph schumpeter theory