A STATISTICS PROJECT PART 3

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ASTATISTICSPROJECT PART 3

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PROJECTPART 3

  1. 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 test-statistic. 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.

  1. 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:&nbspthestudents’ academic performance means are not all equal

Step3: State the Alternative Hypothesis.

Thealternate hypothesis is stated for instance:

Ha:&nbspthestudents’ 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&nbspα.

Todepict what chances the hypothesis has to survive the test, acontingencytable has to be drawn as shown below:

&nbsp

In Reality

Decision

H0&nbspis TRUE

H0&nbspis FALSE

Accept H0

OK

β&nbsp= Type II Error probability

Reject H0

α&nbsp= Type I Error probability

OK

Itis appropriate if the research sets the α&nbspbeforethe 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.&nbsp

Step6: Calculate a test statistic.

Fordefinite treatment level means, F&nbspstatisticis used, and the F-valuegot from the data analysis know as&nbspFcalculated.

&nbspStep7: Construct the model of accepted and rejected regions.

Fromthe Fcalculated.,the critical value of&nbspF&nbsp(Fcritical&nbspor&nbspF)is easily established from the standardized statistical tables.&nbspThe critical value depicts the minimum value for the F test(test-statistic) and thus gives a prediction on whether to reject oraccept the null hypothesis.&nbspThis could be shown in a diagram asfollows

Step8: getting the conclusion about the null hypothesis (H0).

Fromthe analysis, should the Fcalculated&nbspbelarger than the set Fα, then the null hypothesis is rejected as itexists in the rejection region and thus accept the alternatehypothesis HA.

  1. When performing the eight steps for hypothesis testing, which method do you prefer P-Value method or Critical Value method? Why?

Iprefer the P-value 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 p-value method helps todetermine the area (P) in the tail beyond the sample data andcompares it to the t α with the provide significance level.

  1. 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&nbsp± = 0.05 and assume your data is normally distributed and σ is&nbspunknown.

mean

61.81667

Median

61.5

Mode

69

Range

41

Mid-range

20.5

Variance

78.31639

Standard Deviation

8.849655

    1. Write the null and alternative hypothesis symbolically and identify which hypothesis is the claim.

H0=65

Ha&lt65

    1. Is the test two-tailed, left-tailed, or right-tailed?

Thetest is the left tailed this is due to the test claim that falls onthe left side of the graph.

    1. Which test statistic will you use for your hypothesis test z-test or t-test?

Iused t- test simply because the test entails that the Population isnormal, and the variance unknown and also the sample is n&gt30

    1. What is the value of the test-statistic?

AccordingtoBickeland Doksum (2015) the t statistic is given by

    1. What is the P-value?

0.005is between 0.0025 thus &lt 0.05

    1. What is the critical value?

    1. What is your decision reject the null or do not reject the null?

Rejectthe null hypothesis

    1. Explain why you made your decision including the results for your p-value and the critical value.

Thep-value 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.

    1. State the conclusion in non-technical 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., &amp Doksum, K. A. (2015).&nbspMathematicalStatistics: Basic Ideas and Selected Topics, Volume I&nbsp(Vol.117). CRC Press.

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