Is there a relationship between confidence intervals and two

Last updated: 2/14/2024

Is there a relationship between confidence intervals and two tailed hypothesis tests Let c be the level of confidence used to 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 A corresponding relationship between confidence intervals and two tailed hypothesis tests also is valid for other parameters such as p or P P which we will study later Whenever the value of k given in the null hypothesis falls outside the c 1 a confidence interval for the parameter we reject Ho For example consider a two tailed hypothesis test with a 0 01 and Ho 20 H 20 A random sample of size 33 has a sample mean x 23 from a population with standard deviation 6 a What is the value of c 1 a 0 99 For a two tailed hypothesis test with level of significance a and null hypothesis Ho H 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 Construct a 1 x 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 20 31 25 69 What is the value of a given in the null hypothesis i e what is k k 20 Is this value in the confidence interval Yes No OO Do we reject or fail to reject H based on this information We fail to reject the null hypothesis since 20 is not contained in this interval We fail to reject the null hypothesis since 20 is contained in this interval We reject the null hypothesis since 20 is not contained in this interval We reject the null hypothesis since 20 is contained in this interval OO 6 Ucing methods of this chanter find the value for the hypothecis test Bound your SOCIOE to four decimal places