ASTATISTICSPROJECT PART 3
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PROJECTPART 3

Discuss the process for hypothesis testing.
Theprocess of hypothesis entails unknown truth on the initial research,and this gives the researcher to carry out research with a realisticnull and alternate hypothesis as his research will be focused aroundthe stated hypothesis. The researcher makes assumptions on a samplein carrying out the test, and he should pick a perfect test methodand state the ideal teststatistic. The test statistic should bederived about the null hypothesis and the assumptions made earlier onbefore the research. The research should pick the effective alpha (α)value as this will predict the probability that any hypothesis couldbe rejected or accepted. This will yield the test distribution with Tpossible values based on values that could have the null hypothesisrejected thus creating a critical region. From the T valuesgenerated, one can reject or accept the null hypothesis and lastlyconclude his outcome of the research in respect of the test results.

Discuss the eight steps of hypothesis testing?
Step1: entails the understanding of the research objective and thehypothesis to be measured.
Step:2 the Null Hypothesis is stated and defined. The null hypothesis setby the researcher is always the opposite of the working or alternatehypothesis. Thus at the end of the research and test, there is muchhope that the null hypothesis could be rejected.
Forinstance:
Ho: thestudents’ academic performance means are not all equal
Step3: State the Alternative Hypothesis.
Thealternate hypothesis is stated for instance:
Ha: thestudents’ academic performance means are all equal
Thisis to ensure that if the null hypothesis is rejected there are highchances of the alternate hypothesis to be accepted
Step4: Set α.
Todepict what chances the hypothesis has to survive the test, acontingencytable has to be drawn as shown below:
  
In Reality 

Decision 
H_{0} is TRUE 
H_{0} is FALSE 
Accept H_{0} 
OK 
β = Type II Error probability 
Reject H_{0} 
α = Type I Error probability 
OK 
Itis appropriate if the research sets the α beforethe experiment to be 0.05 thusestablish the possibility of having 95% confidence level.
Step5: data collection
Datacould be collected through observation or experimental design. Inmany cases for the test to be carried out there should be real datacollection in respect to the effective research design set by theresearcher. 
Step6: Calculate a test statistic.
Fordefinite treatment level means, F statisticis used, and the Fvaluegot from the data analysis know as F_{calculated}.
 Step7: Construct the model of accepted and rejected regions.
Fromthe F_{calculated}.,the critical value of F (F_{critical} or F)is easily established from the standardized statistical tables. The critical value depicts the minimum value for the F test(teststatistic) and thus gives a prediction on whether to reject oraccept the null hypothesis. This could be shown in a diagram asfollows
Step8: getting the conclusion about the null hypothesis (H_{0)}.
Fromthe analysis, should the F_{calculated} belarger than the set Fα, then the null hypothesis is rejected as itexists in the rejection region and thus accept the alternatehypothesis H_{A}.

When performing the eight steps for hypothesis testing, which method do you prefer PValue method or Critical Value method? Why?
Iprefer the Pvalue method as this is simplest of all and it isdigitally based by calculators when compared to the critical valueapproach that uses the classical tables. The pvalue method helps todetermine the area (P) in the tail beyond the sample data andcompares it to the t α with the provide significance level.

If you selected Option 2: Original Claim: The average age of all patients admitted to the hospital with infectious diseases is less than 65 years of age. Test the claim using α ± = 0.05 and assume your data is normally distributed and σ is unknown.
mean 
61.81667 
Median 
61.5 
Mode 
69 
Range 
41 
Midrange 
20.5 
Variance 
78.31639 
Standard Deviation 
8.849655 

Write the null and alternative hypothesis symbolically and identify which hypothesis is the claim.
H_{0}=65
H_{a}<65

Is the test twotailed, lefttailed, or righttailed?
Thetest is the left tailed this is due to the test claim that falls onthe left side of the graph.

Which test statistic will you use for your hypothesis test ztest or ttest?
Iused t test simply because the test entails that the Population isnormal, and the variance unknown and also the sample is n>30

What is the value of the teststatistic?
AccordingtoBickeland Doksum (2015) the t statistic is given by

What is the Pvalue?
0.005is between 0.0025 thus < 0.05

What is the critical value?

What is your decision reject the null or do not reject the null?
Rejectthe null hypothesis

Explain why you made your decision including the results for your pvalue and the critical value.
Thepvalue is small, and thus we have evidence to reject the nullhypothesis. That is, we fail to reject the alternate hypothesis that: The average age of all patients admitted to the hospital withinfectious diseases is less than 65 years of age.

State the conclusion in nontechnical terms.
Thesample data supports the claim that the average age of all patientsadmitted to the hospital with infectious diseases is less than 65years of age.
References
Bickel,P. J., & Doksum, K. A. (2015). MathematicalStatistics: Basic Ideas and Selected Topics, Volume I (Vol.117). CRC Press.