1. Sample size(n)=60 population mean (µ0 ) =1.73

Samplemean (=1.5 standard deviation=1.12

  1. It`s a one-tailed hypothesis test. We are concerned with the product preventing cavities

  2. HO0 =1.73


  1. Critical test statistics obtained

ZObt = =-1.590689589

  1. Test statistics


  1. Since test statistics value is not less than critical statistic value, the null hypothesis, H0, should not be rejected. The result fails to support the claim that the mean number of cavities of the tooth is less than 1.73 with the new toothpaste.

  2. 95% interval confidence on the mean of the population.

Confidence I. = S. mean ± Z ×SEM, S. mean = 1.500,

Z = 1.96, -1.96

SEM = 1.120 / √ 60 .0= 1.120 /7.75 = 0.15

CI = (-1.33, 4.33)negativecavities excluded, the confidence interval is

0 to 4.334

  1. The critical value is negatively related to the degrees of the critical value reduces the degree of freedom rises. Taking a look at the computed test statistics and corresponding critical value with degree of freedom=13.the percentage of failing to reject the null is high, even though it has to be rejected.


  1. It is a two-tailed hypothesis test since no direction is indicated by the difference.

  2. HOcmpop andHA: µcm ≠µpop

  3. t = ( M – μ) / SEM

= (59 – 58) / 1.016

= 0.984

  1. test statistics with 13 d.f = ±2.160

  2. The researcher should fail to reject the null hypothesis. There is no statistical significance to support the claim.

  3. Confidence. I = S.mean ± Tcv. SEM

= 59.0 ±2.16(1.05)

CI =( 56.805 ,61.195 )


  1. χ2 = Σ ( Obs– Exp) 2 / Exp = (31-24) 1 / 12 + (89.0 – 96.0)

1/ 36

= 2.042 + 0.510

χ2 obtained = 2.552

  1. the degree of freedom is one that is 2-1=1

  2. test statistics χ2 =3.84

  3. Since χ2 obtained = 2.552is less than test statistics χ2 =3.84 the null hypothesis should not be rejected. The evidence availlable fails to support the claim.


  1. The research fulfills the assumptions of independent group testing using one-tailed hypothesis test.

  2. H0: μ NM ≥ μ M us and H1: μNM &lt μ Mus

  3. Tcv = 1.860

T (16) obtained = 2.19

P is less than 0.05, one-tailedhypothesis testing(SPSS obtained value.)


The H0should be rejected, and make conclusion that learning in absencemusic enhances better devotion on the material.

e. r2 = (T2 / T2) + degrees offreedom

= 2.193 / 2.193+ 8

R 2 is 0.38 in case of a bigeffect size.


  1. t test assumption on groups that are correlated is met in this research

  2. H0: μ NM ≥ μ Mus and H1: μ NM &lt μ Mus

  3. Tcv = 2.02

  4. t(5) obtained = 2.74

P is less than 0.05,

(Excel figure.)

D) The null hypothesis should berejected .there is enough evidence to support the claim that studyingin an absence of music betters results.

e)r2 = T2 / T2 + degress of freedom = 2.739 divided by (2.739 + 5)

r2 is equal to 0.12 in case of bigger effect size.


g)Confidence Interval = Mean1 – Mean2 ± tcv(s Mean1 – Mean2)

= 7.667 – 6.66 ± 2.015 ×(0.494 – 0.33)

= 1 ± 2.015 × 0.161 = 1 ±0.324

CI = 0.676 to 1.324


  1. Wilcoxon rank sum test assumptions on one tailed test have been met in this study.

  2. H0: μ gs ≥ μ rest and H1: μ gs &lt μ rs

  3. W (n1=7, n2=7) cv = 39

W(n1 = 7, n2 = 7)


p= 0.05,

One-tailedhypothesis test


7 .0




























  1. Do not reject the null hypothesis. Test scores in the two sources have no much statistical difference.


A). χ2 (1, n = 105)


p&lt 0.05

men women expectation

front 15.027.0 42.0 21.2 20.8

back32.0 19.0 51.0 25.025.2

47.0 46.0

Chi-square= 6.73 with d.f =1

b)degrees of freedom =(2-1) ×(2-1)=1

c)χ2cv= 3.84

d)thenull hypothesis should be rejected. There is enough evidence insupport of the claim that preferences on seating amid men and women,back row are mostly occupied with men and front row women.

Part1, question two

Degreesof freedom:refers to the figures concerning the scores in a sample data whichare perceived to vary freely. On a particular mean figure, the valuescan vary at liberty in keeping the mean same except the last value.Theseare the independent figures of data used in a computation. It is usedto know the precision of the sample population used in an inquiry.The greater the degree of freedom, the more the likelihood of thewhole population to be tested precisely

Calculationof the degrees of freedom:they can be computed by subtracting the number of independent scoresthat calculates the random scores from one parameter estimate that isN-1.but this depends on with the kind of data we have. We have otherways for computing d.f like:

Twosample test, d.f =n1+n2-1

Simplelinear regression

d.f= n -2

chi-squareof a goodness of fit test

d.f= k-1

chi=squarehomogeneous test

(columnnumber -1)(Row number -1)

Inferentialstatistics allowance on inferencing:inferential statistics allows the research to have his opinion aboutthe population based on sample data parameters in the researchpreceding particular statistical procedures and sampling on thepopulation.

GeneralLinear Model and its importance:GLM unifies several models of statistics into a generalization thatis much more flexible of linear regression. Keeping in mind the goalof data analysis. To present in a short way what is happening in aparticular data that is given. The capability is enhanced by the GLM.Desperate tools of statistics have been brought into one by the GLM.It has led to advancement in statistical models, such as coming upwith SEM alongside with HLM, for assessing models that seemcomplicated.

Comparisonand contrast between parametric and non-parametric statistics, andunique cases for their deployment: whenit comes to ratio data or interval statistics, parametric statisticsare used. The following conditions must be met for one to useparametric statistics: the data must be of normal distributionforming a bell-shaped, the population standard deviations and meansknow or can be computed. Parametric statistics give accurate andestimates that are more precise than their nonparametric counterpartswhen assumptions have been met. They have an element of possibilitiesand prediction of the scores.

Onthe other hand, nonparametric statistics are mainly used in thefollowing situations: during ranking of data, in cases whereassumptions on distribution are not permitted and preferenceassessment.

Theimportance of paying attention to test statistics assumptions andoptions available if dependent variable scores are not distributednormally:when it comes to parametric tests, they only give accurate results ifthe assumptions have been met. Carrying out these tests withoutconforming them to the assumptions leads to misleading and inaccurateresults. In cases where dependent variable scores do not meet theassumption of normality in their distribution, however, they metother hypotheses, such as bell-shaped, a t-test parametric that canbe used in such cases. But where they are not bell-shaped in additionto them lacking normal distribution, the only option here is to usenonparametric statistical tests.


  1. P=0.05

Itcan be referred to as alpha. In statistics, the level ofsignificance. Here p standards for the likelihood of type I errorbeing committed(Schmidt, 2010).That is, rejecting a true null hypothesis.Schmidt(2010) there is six misconceptions identified when it comes to thelevel of significance.

  1. Reliable replication

  2. Size of relationship identification

  3. No relationship is indicated when there is no significance indication.

  4. There are so essential to research works

  5. Guarantee neutrality

  6. Makes a contribution to the field of investigation.

Inreality, significance has no association on reproduction itdesignates in circumstances where there exist no association amongthe variables. Normally there exist a 1.200 probability whichsignificance will be found. Type one and type two errors areindependent of statistical significance which can easily bemanipulated by the sample size. For this reason, it is not theaccurate measure when it comes to summarizing works of statistical.In addition, it does not guarantee the neutrality of data. It isestablished in cases where null hypothesis are used in multiples,which reduces the significance level.

  1. Comparison of size and significance level in statistics

Thereexist four aspects of statistical power in any set of data that oneis given. Those are size effect, a size of the sample, a level ofthe significance and lastly the power. Many studies have concentratedmost of their efforts and focus on the degree of importance. It hascreated an exclusion of other aspects of the statistics. The primarygoal underlying any analysis of statistical work is an establishmentof independent populations with differences that can be quantified(Carver, 1978).Effect size refers to a measurement indicating the degree of theexperimental mean that is projected to differ from the control mean.Significance refers to the maximum risk that is allowed on committinga type I error that is, rebuffing a null hypothesis that is true.Both work in a similar manner. As they reduce, the minimum size of asample has to increase for sufficient power keeping a result that issignificant. On another hand increment in value of the two, resultsin a reduction of the minimum size of the sample in keeping powerconsistent. But this is the only similarity they share. Apart fromit, effect size and statistical significance have no relationship atall.

  1. Statistical significance and clinically significant results

Occasionallyone to twenty times statistical significant outcomes happen just dueto chance even in cases where the null is false. The significance isadvantageous in the increasing and expanding field knowledge.Statistical merits tell us how the outcome from the field differsfrom a mean of the population alongside the likelihood it does nothappen just owing to chance. According to Schmidt (2010), arguedforward result of the meta-analysis. The 8 studies were statisticalnon-significant while the rest were significant. The analysis is agood example of the significance of practical nature since it led toa single value.

  1. NHST

Nullhypothesis significance testing makes an assumption on the nullhypothesis means to be happening due to principally on samplingvariation. The null is rejected in circumstances where the results ofstatistical significance are identified.

  1. NHST criticism

  1. Answering the wrong question

  2. The exercise is trivial

  3. It takes an ordinal value in the ratio value

Itleads to deviation from addressing the issue of validity andreliability. Based on the assumption of the NHST in most cases thenull hypothesis will always be false. It brings sample size andlikelihood preceding the clinical significance.

  1. NHST alternatives

Analternate to NHST anticipated by Schmidt is to trail the physicalscientist’s example and exploit interval of confidence. Heproposes that trust confidence intervals give elaborate informationas compared to the tests of significance though they happen to beobjective. As well he cites significance test on 1999 APA Task ForceReport that confidence intervals ought to be presented in studyoutcomes. Kirk (2003) recognized that confidence intervals give restof the data related with benefits, nevertheless also contains &quotavariety of figures in which the parameters of the population isprobably to present a lie.


Carver,P. (1978). The Case Against Statistical Significances Test. HarvardEducational-Review, 48, 378-399.

Cohen,J. (1992). A Power Primer. Psychological Bulletin, 112(1), 155-159.doi:10.1037/0033-2909.112.1.155

Faull,F., Erdfelder, E., Lang, A.-G., &amp Buchneer, A. (2007). G*Power 3:A Flexible Statistical Power Analysis Program For The Social,Behavioral, Biomedical SCIENCES. BEHAVIOR RESEARCH METHODS, 39(2),175-191.

Jackson,S. L. (2012). Research methods and statistics: A Critical ThinkingApproaches (4th Ed.). Belmont, CA: Wadsworth Cengage Learning.

Kirk,R. E. (2003). The importance of effect magnitude. In S. F. Davis(Ed.), Handbook of Research Methods in Experimental Psychology (pp.83-105). doi:10.1002/9780470756973.ch5

Schmidt,F. (2010). Detecting, Correcting lies that data tell. Perspectives onPsychological Science, 5(3), 233-242. Doi: 10.1177/1745691610369339

Trochim,W. M. K., &amp Donnelly, J. P. (2008). The research MethodsKnowledge Base (3rd Ed.). Mason, OH: Cengage Learning.