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 ? 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 ? and null hypothesis H0: ? = k, we reject H0 whenever k falls outside the c = 1 − ? confidence interval for ? based on the sample data. When k falls within the c = 1 − ? confidence interval, we do not reject H0.(A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, ?1 − ?2, or p1 − p2, which we will study later.) Whenever the value of k given in the null hypothesis falls outside the c = 1 − ? confidence interval for the parameter, we reject H0. For example, consider a two-tailed hypothesis test with ? = 0.01 andH0: ? = 20 H1: ? ≠ 20A random sample of size 38 has a sample mean x = 23 from a population with standard deviation ? = 5. 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 hypothesisHo: u = k, we reject H, whenever k falls outside the c = 1- a confidence intervalfor u based on the sample data. When k falls within the c = 1 - a confidenceinterval, we do not reject Ha:(A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, u, - Ha, or p. - Pa, 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 H.. Forexample, consider a two-tailed hypothesis test with a = 0.01 andHo: 4 = 20H: u = 20A random sample of size 38 has a sample mean x = 23 from a population with standard deviation o = 5.(a) What is the value of c = 1 - a?Construct a 1 - a confidence interval for u from the sample data. (Round your answers to two decimal places.)lower limitupper limitWhat is the value of u given in the null hypothesis (i.e., what is k)?k =Is this value in the confidence interval?O YesO NoDo we reject or fail to reject H, based on this information?O we fail to reject the null hypothesis since u = 20 is not contained in this interval.O we fail to reject the null hypothesis since u = 20 is contained in this interval.O we reject the null hypothesis since u = 20 is not contained in this interval.O we reject the null hypothesis since u = 20 is contained in this interval.(b) Using methods of this chapter, find the P-value for the hypothesis test. (Round your answer to four decimal places.)Do we reject or fail to reject H,?O we fail to reject the null hypothesis since there is sufficient evidence that u differs from 20.O we fail to reject the null hypothesis since there is insufficient evidence that u differs from 20.O we reject the null hypothesis since there is sufficient evidence that u differs from 20.O we reject the null hypothesis since there is insufficient evidence that u differs from 20.Compare your result to that of part (a).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).O These results are the same.

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Given a two tailed hypothesis test with α=0.01 H0 : μ=20 Vs H1 : μ≠20 And a sample of size n=38,…

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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 Hg: -k, we reject H, whenever k falls outside the c-1-a confidence interval for u based on the sample data, When k falls within the c1-a confidence interval, we do not reject H (A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, , - a, or p, - Pa, which we will study later.) Whenever the value of k given in the null hypothesis falls outside the e-1-a confidence interval for the parameter, we reject H. For example, consider a two-tailed hypothesis test with e 0.01 and Me:- 20 A random sample of size 38 has a sample mean x- 23 from a population with standard deviation e- 5. H 20 (a) What is the value of e -1- a? Construct a 1 - a confidence interval for a from the sample data. (Round your answers to two decimal places.) lower limit upper limit What is the value of a given in the nul hypothesis (i.e., what is k)? k- Is this value in the confidence interval? O Yes O No Do we reject or fail to reject H, based on this information? O We fail to reject the null hypothesis since - 20 is not contained in this interval. O we fail to reject the null hypothesis since - 20 is contained in this interval. O We reject the null hypothesis since a- 20 is not contained in this interval. O we reject the null hypothesis since u 20 is contained in this interval. (b) Using methods of this chapter, find the Pvalue for the hypothesis test. (Round your answer to four decimal places.) Do we reject or fail to reject H,? O we fail to reject the null hypothesis since there is sufficient evidence that a differs from 20. O we fail to reject the null hypothesis since there is insufficient evidence that differs from 20. O we reject the null hypothesis since there is sufficient evidence that differs from 20. O we reject the null hypothesis since there is insufficient evidence that a differs from 20. Compare your result to that of part (a). 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). O These results are the same.

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 Hg: -k, we reject H, whenever k falls outside the c-1-a confidence interval for u based on the sample data, When k falls within the c1-a confidence interval, we do not reject H (A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, , - a, or p, - Pa, which we will study later.) Whenever the value of k given in the null hypothesis falls outside the e-1-a confidence interval for the parameter, we reject H. For example, consider a two-tailed hypothesis test with e 0.01 and Me:- 20 A random sample of size 38 has a sample mean x- 23 from a population with standard deviation e- 5. H 20 (a) What is the value of e -1- a? Construct a 1 - a confidence interval for a from the sample data. (Round your answers to two decimal places.) lower limit upper limit What is the value of a given in the nul hypothesis (i.e., what is k)? k- Is this value in the confidence interval? O Yes O No Do we reject or fail to reject H, based on this information? O We fail to reject the null hypothesis since - 20 is not contained in this interval. O we fail to reject the null hypothesis since - 20 is contained in this interval. O We reject the null hypothesis since a- 20 is not contained in this interval. O we reject the null hypothesis since u 20 is contained in this interval. (b) Using methods of this chapter, find the Pvalue for the hypothesis test. (Round your answer to four decimal places.) Do we reject or fail to reject H,? O we fail to reject the null hypothesis since there is sufficient evidence that a differs from 20. O we fail to reject the null hypothesis since there is insufficient evidence that differs from 20. O we reject the null hypothesis since there is sufficient evidence that differs from 20. O we reject the null hypothesis since there is insufficient evidence that a differs from 20. Compare your result to that of part (a). 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). O These results are the same.

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For a two-tailed hypothesis test with level of significance ? and null hypothesis H₀: ? = k, we reject H₀ whenever k falls outside the c = 1 − ? confidence interval for ? based on the sample data. When k falls within the c = 1 − ? confidence interval, we do not reject H₀.

(A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, ?₁ − ?₂, or p₁ − p₂, which we will study later.) Whenever the value of k given in the null hypothesis falls outside the c = 1 − ? confidence interval for the parameter, we reject H₀. For example, consider a two-tailed hypothesis test with ? = 0.01 and

H₀: ? = 20 H₁: ? ≠ 20

A random sample of size 38 has a sample mean x = 23 from a population with standard deviation ? = 5.

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: u = k, we reject H, whenever k falls outside the c = 1- a confidence interval
for u based on the sample data. When k falls within the c = 1 - a confidence
interval, we do not reject Ha:
(A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, u, - Ha, or p. - Pa, 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 H.. For
example, consider a two-tailed hypothesis test with a = 0.01 and
Ho: 4 = 20
H: u = 20
A random sample of size 38 has a sample mean x = 23 from a population with standard deviation o = 5.
(a) What is the value of c = 1 - a?
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?
O Yes
O No
Do we reject or fail to reject H, based on this information?
O we fail to reject the null hypothesis since u = 20 is not contained in this interval.
O we fail to reject the null hypothesis since u = 20 is contained in this interval.
O we reject the null hypothesis since u = 20 is not contained in this interval.
O we reject the null hypothesis since u = 20 is contained in this interval.
(b) Using methods of this chapter, find the P-value for the hypothesis test. (Round your answer to four decimal places.)
Do we reject or fail to reject H,?
O we fail to reject the null hypothesis since there is sufficient evidence that u differs from 20.
O we fail to reject the null hypothesis since there is insufficient evidence that u differs from 20.
O we reject the null hypothesis since there is sufficient evidence that u differs from 20.
O we reject the null hypothesis since there is insufficient evidence that u differs from 20.
Compare your result to that of part (a).
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).
O These results are the same.

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