# This week, we consider how to

This week, we consider how to conduct hypotheses test on one sample data. Discuss the concepts associated with these tests. Consider the following:

• The difference between a one tail and a two tailed test.
• The importance of stating the null and alternative hypotheses before conducting the test.
• The importance of a type one error (p) in conducting the test
• The relationship between the p value and our decision to accept or reject the null hypothesis

Difference between One-tailed and Two-Tailed in any test, thecritical region is represented by a portion at the area under theprobability curve of the sampling distribution af test statisticimportant to state alternative hypothesis to know our rejectionregion more precisely By the use of critical region and alternativehypothesis we decide whether the test is one-tailed or two- tailed.A test in which the alternative hypothesis is one-tailed eitherright-tailed or left-tailed) is called one- talled test Ee a testfor testing mean of a population Ho: against the alternativeImportance of type -1 error: By using the size of type-l error vizawe could know our level of significanca’.The size of typal error asknown as level of significance level of significance means theprobability that random value of the statistic belongs to criticalregion. The level of significance is always foed in advance befarecollecting sample information. hypothesis: Hi: suo Iright-tailed!or Hi: Mollelt-tailed), is a single tailed test. In other words wecan say that if critical region of test lies only in one side ofthe curve of the sampling distribution af test statistic, then thetest is one-tailed test. The relationship between the p value andour decision to accept or reject the null hypothesis: Aftercollecting the sample values we imply those sample values in ourchansen test statistic, doing this we get the same value from thetest statistic.we compare the computed value of test statistic withthe significant value of Za(tabulated at the given level ofsignificance if the the value of test statistic is less the thevalue of Za we accept our Null Hypothesis otherwise we reject thevalues of Zo is different for different values of a thats therelationship between p value and our decision. In other we can saythat if a is 0.05 then we can say that there is 0.05 chances out of1 that we are making a wrong decision. www. m eta for relerencethis the curve we are talking about in this situation we haveraight tailed test because the rejection region is in the rightside of the curve. Similarly a test in which the alternativehypothesis is twa tailed is considered as a two-tailed test herethe rejection region is in the both of the side of curve. Fg: atest for testing mean of a population Ho: Pl=hlo against thealternative hypothesis: Hi: H#Mo (H1>Mo and H1: Haplo), is adouble-talled test. Importance of stating Hypothesis beforeconducting test: Stating hypothesis is important because having setup the null hypothesis we compute the probability P that thedeviation between the observed sample statistic and thehypothetical parameter value might have occurred due to fluctuationof sampling. In other words by setting up the null hypothesis wecan check that the difference between the sample statistic andpopulation parameter is just due to chance or the phenomenon willreflect in long run also.Also, as discussed earlier it is

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