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.)

Name: Is there a relationship between confidence intervals and two-tailed hy
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
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.

Answered: consider a two-tailed hypothesis test…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Topic Video

Question

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.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Means$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.