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: H = 21 H1: H# 21 A random sample of size 31 has a sample mean x = 20 from a population with standard deviation o = 8. (a) What is the value of c = 1 - a? Using the methods of Chapter 7, construct a 1 - a confidence interval for u from the sample data. (Round your answers to two decimal places.) lower limit upper limit What is the value of u given in the null hypothesis (i.e., what is k)? k =

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Author:Amos Gilat
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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.
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
µ 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, µ1 - H2, or P1 - P2, which we will study in later sections.) 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: H = 21
H1: µ # 21
A random sample of size 31 has a sample mean x = 20 from a population with standard deviation o = 8.
(a) What is the value of c = 1 - a?
Using the methods of Chapter 7, construct a 1 - a confidence interval for u from the sample data. (Round your answers
to two decimal places.)
lower limit
upper limit
What is the value of u given in the null hypothesis (i.e., what is k)?
k =
Is this value in the confidence interval?
Transcribed Image Text: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. 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 µ 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, µ1 - H2, or P1 - P2, which we will study in later sections.) 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: H = 21 H1: µ # 21 A random sample of size 31 has a sample mean x = 20 from a population with standard deviation o = 8. (a) What is the value of c = 1 - a? Using the methods of Chapter 7, construct a 1 - a confidence interval for u from the sample data. (Round your answers to two decimal places.) lower limit upper limit What is the value of u given in the null hypothesis (i.e., what is k)? k = Is this value in the confidence interval?
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