construct a confidence interval from sample data Let a be
Last updated: 2/14/2024
construct a confidence interval from sample data Let a be the level of significance for a two tailed hypothesis test The following statement applies to hypothesis tests of the mean For a two tailed hypothesis test with level of significance a and null hypothesis Ho k we reject Ho whenever k falls outside the c 1 a confidence interval for based on the sample data When k falls within the c 1 a confidence interval we do not reject Ho A corresponding relationship between confidence intervals and two tailed hypothesis tests also is valid for other parameters such as p M M or P P which we will study in later sections Whenever the value of k given in the null hypothesis falls outside the c 1 alpha confidence interval for the parameter we reject Ho For example consider a two tailed hypothesis test with 0 05 and Hoi H 21 H 21 A random sample of size 13 has a sample mean x 22 from a population with standard deviation 8 a What is the value of c 1 a 0 95 Using the methods of Chapter 7 construct a 1a confidence interval for from the sample data Enter your answer in the form lower limit to upper limit Include the word to Round your numerical answers to two decimal places X What is the value of given in the null hypothesis i e what is k k 21 Is this value in the confidence interval Yes O No Do we reject or fail to reject H based on this information Fail to reject since 21 is not contained in this interval O Fail to reject since 21 is contained in this interval O Reject since 21 is not contained in this interval O Reject since 21 is contained in this interval b Using methods of Chapter 8 find the P value for the hypothesis test Round your answer to four decimal places P value Do we reject or fail to reject Ho O Reject the null hypothesis there is sufficient evidence that differs from 21 O Fail to reject the null hypothesis there is insufficient evidence that differs from 21 O Fail to reject the null hypothesis there is sufficient evidence that differs from 21 O Reject the null hypothesis there is insufficient evidence that differs from 21 Compare your result to that of part a These results are the same O We rejected the null hypothesis in part b but failed to reject the null hypothesis in part a O We rejected the null hypothesis in part a but failed to reject the null hypothesis in part b