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: μ = k, we reject H0 whenever k falls outside the c = 1 – α confidence interval for μ based on the sample data. When k falls within the c = 1 – α 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, μ1 − μ2, 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 – α confidence interval for the parameter, we reject H0. For example, consider a two-tailed hypothesis test with ? = 0.01 andH0: μ = 21H1: μ ≠ 21A random sample of size 20 has a sample mean x = 19 from a population with standard deviation σ = 7. (b) Using methods of Chapter 8, find the P-value for the hypothesis test. (Round your answer to four decimal places.)

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Description: 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

In this context, the aim is to check whether the organization’s burnout levels are significantly less than a mean of 50. The test hypotheses are given below: The Null hypothesis H0: µ = 21 The Alternative hypothesis H1: µ≠21. It is given that the level of significance is 0.01. In this context, the general population of individuals has a mean of 21, a standard deviation of 7, and follows a normal curve. The population standard deviation is known. Thus, the appropriate test is one sample z test. The type of test statistic is one sample z test. Denote µ as the true mean.Computation of test statistic value: The formula for one sample z test is given below. z=x̅-µσn Calculation: Here, = 19, µ =21, σ =7, and n is 20. By substituting these values in z formula, the test statistic value is obtained as given below: z=19–21720=–1.28 The value of test statistic –1.28. The P-value for two-tailed test is obtained as given below: 2×Pz≤-1.28=2×0.1003Using Standard normal table=0.2006 Therefore, the P-value is 0.2006. Since the P-value is greater than the significance level of 0.01, the null hypothesis is not rejected.

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher: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 ? 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: μ = k, we reject H₀ whenever k falls outside the c = 1 – α confidence interval for μ based on the sample data. When k falls within the c = 1 – α 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, μ₁ − μ₂, 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 – α confidence interval for the parameter, we reject H₀. For example, consider a two-tailed hypothesis test with ? = 0.01 and

H₀: μ = 21
H₁: μ ≠ 21

A random sample of size 20 has a sample mean x = 19 from a population with standard deviation σ = 7.

(b) Using methods of Chapter 8, find the P-value for the hypothesis test. (Round your answer to four decimal places.)

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