Question

 

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

Answer 1

Difference between One-tailed and Two-Tailed in any test, the critical region is represented by a portion at the area under the probability curve of the sampling distribution af test statistic important to state alternative hypothesis to know our rejection region more precisely By the use of critical region and alternative hypothesis we decide whether the test is one-tailed or two- tailed. A test in which the alternative hypothesis is one-tailed either right-tailed or left-tailed) is called one- talled test Ee a test for testing mean of a population Ho: against the alternative Importance of type -1 error: By using the size of type-l error viza we could know our level of significanca'.The size of typal error as known as level of significance level of significance means the probability that random value of the statistic belongs to critical region. The level of significance is always foed in advance befare collecting sample information. hypothesis: Hi: suo Iright-tailed! or Hi: Mollelt-tailed), is a single tailed test. In other words we can say that if critical region of test lies only in one side of the curve of the sampling distribution af test statistic, then the test is one-tailed test. The relationship between the p value and our decision to accept or reject the null hypothesis: After collecting the sample values we imply those sample values in our chansen test statistic, doing this we get the same value from the test statistic.we compare the computed value of test statistic with the significant value of Za(tabulated at the given level of significance if the the value of test statistic is less the the value of Za we accept our Null Hypothesis otherwise we reject the values of Zo is different for different values of a thats the relationship between p value and our decision. In other we can say that if a is 0.05 then we can say that there is 0.05 chances out of 1 that we are making a wrong decision. www. m eta for relerence this the curve we are talking about in this situation we have raight tailed test because the rejection region is in the right side of the curve. Similarly a test in which the alternative hypothesis is twa tailed is considered as a two-tailed test here the rejection region is in the both of the side of curve. Fg: a test for testing mean of a population Ho: Pl=hlo against the alternative hypothesis: Hi: H#Mo (H1>Mo and H1: Haplo), is a double-talled test. Importance of stating Hypothesis before conducting test: Stating hypothesis is important because having set up the null hypothesis we compute the probability P that the deviation between the observed sample statistic and the hypothetical parameter value might have occurred due to fluctuation of sampling. In other words by setting up the null hypothesis we can check that the difference between the sample statistic and population parameter is just due to chance or the phenomenon will reflect in long run also.Also, as discussed earlier it is

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