Ina case where there exist random numbers from zero to 99. If anindividual needs to pick a random sample of numbers in the container,then place the numbers aside and or replace them back in thecontainer (Mann, & Lacke, 2010). On the other hand, if theindividual places back the number in the bowl then it may be selectedone more time again but if it is placed aside, then it can only beselected once. Then this process is defined as Sampling withReplacement.
Considera container with 100 unique digits from zero to ninety-nine, then anindividual would like to select a random sample of digits in thecontainer. After selecting the digits in the container, then selectone digit and place it aside or replace it again in the container. Ifthe digit is returned to the container, then it will be selected morethan one time unlike when placed aside that can only be picked onetime.
Practically,sampling with replacement the two digits are completely independent.Ideally, this is an indication that the first outcome affects thesecond outcome. Mathematically this covariance is nil.
Inthis case, Foofy has calculated the x̅ (MEAN) of her data. However,this is a random sample from the given population of Q. This iscorrectly done with a zed score of +41 from the distribution of thedata Q. However, this is not correct since her data is not a randomsample from the entire population Q. On top of that, her computedcorrelations from the population comparing an individual’s physicalstrength compared to the average grade attained. Naturally, acomputer provides her total correlation from the sample of the 200individuals this value is r (1999) = +.09, p=<0.001. This is thebest method of predicting the kind of individual an applicant is morelikely to succeed in academics. However, r= 0.09 accounts for alittle value in the variability that is less than one a useful toolfor predicting the success of the college.
Consideringthat the mean uis 75 and the statistical analysis is on the final exam is1_ (QX=6.4). Then those students who studied statistics are,X=72.The critical value represents the inner edge representing the entirerejection region. In this particular situation, the criterion is0.05, and the every tail is equivalent to 0.025. Therefore, it willbe prudent to equate +=1.96 as the correct critical value for z andthe criterion for 0.05 as the two-tailed tests.
Inthis case from the data collected by the researcher in the sampledata and the test statistics conducted, the statistics fall from awithin the specified range of values and on this note, is prudent toreject the null hypothesis (Wooldridge, 2009). Because the mean is 75from the observed random data and the sample mean is 72 then rejectthe hypothesis. The rejection region represents the region with lessthan 75 or more than 76
Thesample does not represent the typical student’s population this isbecause there exists a huge margin from the mean of 75 and thepopulations mean of 72. A difference of three is a big gap.
Themean of the population is 33, that of the sample population is 36.8,and the total number of observed data is 30
NullHypothesis: The mean population raw scores is 33
AlternativeHypothesis: The mean of the population is not 33
Thelevel of significance in the test and the critical value 0.05
Thecritical value is 0.05
Naturally,the probability of a sample is supposed to represent the populationthat they come from. However, there is a probability of a differencebecause of the random process applied when selecting the samples, inthis case, the observed data is 30 with a mean of 33, whereas thepopulation delinquent is 36.8. At the level of this sample, it isclear that the mean population of the raw scores exceeding 33 arehigher the difference is due to sampling errors inferentialstatistics. However, this difference is too huge due to the basis ofthe chance alone.
Theconclusion from this population is that the difference in the meanfrom the samples and that of the population is very huge indicatingthat the random process selected is very vague.
Consideringthat the mean from the raw population is 28 while that of thepopulation is 34 and the number of observed data is 35. In this case,from the above data collected by the examiner both the sample dataand the test statistics conducted, the statistics does not fall inthe specified range of values and on this note, is prudent to rejectthe null hypothesis (Osborn, 2006). The reason being because the meanis 28 from the random observed data the sample mean of 35 then rejectthe hypothesis. The rejection region represents the region with lessthan 26 or more than 30.
Historically,the number of boys is 105 in every 100 girls a ratio of 1.05 as thesex ratio at the point of conception. The percentage of boys amonggirls is 52.2%. Therefore based on this statistical data, howeverconsidering the fact that the couple has conceived eight daughtersbefore the probability of conceiving a boy is highly unlikely.
Mann,P. S., & Lacke, C. J. (2010). Introductorystatistics.Hoboken, NJ: John Wiley & Sons.
Osborn,C. E. (2006). Statisticalapplications for health information management.Sudbury, Mass: Jones and Bartlett Publishers.
Wooldridge,J. M. (2009). Introductoryeconometrics: A modern approach.Mason, OH: South Western, Cengage Learning.