### Critical Value Calculation#### Problem Statement:Find the critical value $ z_{\alpha/2} $ that corresponds to the given confidence level.#### Given:- **Confidence Level:** 86%#### Required:- Determine the value of $ z_{\alpha/2} $- Round the result to two decimal places as needed.#### Solution:To find this critical value, use the following steps:1. **Determine the Alpha Level**: \[ \alpha = 1 - \text{Confidence Level} = 1 - 0.86 = 0.14 \] 2. **Divide Alpha by 2**: \[ \alpha/2 = 0.14 / 2 = 0.07 \]3. **Find the Complementary Probability**: \[ 1 - 0.07 = 0.93 \] 4. **Use the Z-table**: Find the z-score that corresponds to 0.93 in the standard normal distribution table.5. **Determine $ z_{\alpha/2} $**: - You will find that the value of $ z_{\alpha/2} $ is approximately 1.48 after consulting the Z-table. Hence, the answer is:\[z_{\alpha/2} = 1.48\]---This critical value is essential in determining confidence intervals in statistics. Ensure to accurately locate the z-score corresponding to the cumulative probability from the Z-table to solve similar problems correctly.

Answered: Image /qna-images/answer/be4f48fa-112d-4210-aad8-bfda2a8c40a8.jpg

Answered: Find the critical value za/2 that…

Find the critical value za/2 that corresponds to the given confidence level. 86% Za/2%D Round to two decimal places as needed.)

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

Q: Of 500 random people surveyed, 72 were smokers. Find the 95% confidence interval. SE=0.0157

Q: If n = 100 and p (p-hat) = 0.9, construct a 95% confidence %3D interval. Give your answers to three…

A: Givensample size(n)=100p^=0.9α=1-0.95=0.05α2=0.025zc=zα2=z0.025=1.96 (from z table)

Q: Find tα/2 when n=12 for the 95% confidence interval for the mean.

A: Given information- Sample size, n = 12 Confidence level, c = 0.95 So, significance level (α) = 0.05

Q: Which of the following will decrease the width of a confidence interval I. Increasing the…

A: The confidence interval depends on the three factors: Confidence level: The width of the confidence…

Q: In a survey of 2399 adults in a recent year, 1319 say they have made a New Year's resolution.…

A: Given In a survey of 2399 adults in a recent year, 1319 say they have made a New Year's resolution.…

Q: Assume that population proportion is to be estimated from the sample described. Use the sample…

A: sample size(n)=580 sample proportion(p^)=0.7 confidence level=95%

Q: Find the confidence interval for population correlation coefficient if r = 0.2 and n= 625.

A: The provided information are: Sample correlation coefficient (r) = 0.2 Sample size (n) = 625 No…

Q: Find the level of the confidence interval that has the value %a/2 = 1.96. (Round the final answer to…

A: The objective of this question is to find the level of the confidence interval given that the value…

Q: You sample 40 dogs and find a sample mean weight of 60 lbs with a sample standard deviation of 5.…

A: From the provided information, Sample size (n) = 40 Sample mean (x̅) = 60 lbs Sample standard…

Q: Use the Student's t distribution to find tc for a 0.95 confidence level when the sample is 10.…

A: 95% confidence level Sample size , n = 10 Degrees of freedom = n - 1 Degrees of freedom = 10 - 1 = 9

Q: f n=200 and X=80, construct a 99% confidence interval estimate for the population proportion.

Q: Scored obtained by a large group of students taking a test are known to be normally distributed. A…

A: Here given that n= 25 So mean, X bar = summation Xi /n = 1508/25 = 60.32 Standard deviation, sigma…

Q: Use the Student's t distribution to find tc for a 0.95 confidence level when the sample is 6. (Round…

A: It is given that the sample size is 6.

Q: A simple random sample of 500 elements generates a sample proportion = 0.83. a. Provide the 90%…

Q: Find the critical value z2 that corresponds to the given confidence level. 90%

A: Given ɑ=0.10 We want to find Zɑ/2 =?

Q: tc for a 0.95 confidence level when the sample is 19. (Round your answer to three decimal places.)

A: Given that,

Q: now find the 99% confidence interval given the same information, x=13

A: The given regression equation is y^=7+15x se=10.14X__=7n=22∑Xi-X__2=200

Q: Use the Student's t distribution to

A: From the given information, the confidence level is 0.95 Significance level is 1-0.95=0.05 Given…

Q: The graph below shows a 95% confidence interval for a population proportion that has been estimated…

A: 1. As the sample size increase the margin of error reduces As the margin of error reduces the…

Q: If n = 550 and X = 440, construct a 90% confidence interval for the population proportion, p. Give…

A: Given information:Total number of trials (n) = 550Number of success (X) = 440Confidence level = 0.90

Q: If n=200 and X=70, construct a 99% confidence interval estimate for the population proportion. SIS…

Q: For a confidence level of 80% with a sample size of 23, find the critical t value. Round your answer…

A: Given confidence level =80%sample size(n)=23

Q: Round to three decimal places. For a confidence level of 99%, find the critical z

Q: The 95% confidence interval of the variance of a population is computed as (12.367,21.761).…

A: Given information: The 95% confidence interval for the variance of a population is (12.367, 21.761).…

Q: Construct a 95% confidence interval of the population proportion using the given information.…

Concept explainers

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.

Question

### Critical Value Calculation

#### Problem Statement:
Find the critical value $ z_{\alpha/2} $ that corresponds to the given confidence level.

#### Given:
- **Confidence Level:** 86%

#### Required:
- Determine the value of $ z_{\alpha/2} $
- Round the result to two decimal places as needed.

#### Solution:
To find this critical value, use the following steps:
1. **Determine the Alpha Level**:
\[
\alpha = 1 - \text{Confidence Level} = 1 - 0.86 = 0.14
\]

2. **Divide Alpha by 2**:
\[
\alpha/2 = 0.14 / 2 = 0.07
\]

3. **Find the Complementary Probability**:
\[
1 - 0.07 = 0.93
\]

4. **Use the Z-table**:
Find the z-score that corresponds to 0.93 in the standard normal distribution table.

5. **Determine $ z_{\alpha/2} $**:
- You will find that the value of $ z_{\alpha/2} $ is approximately 1.48 after consulting the Z-table.

Hence, the answer is:
\[
z_{\alpha/2} = 1.48
\]

---

This critical value is essential in determining confidence intervals in statistics. Ensure to accurately locate the z-score corresponding to the cumulative probability from the Z-table to solve similar problems correctly.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Types of Data and Their Measurement$

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.

Similar questions

If n=600 and p^ (p-hat) = 0.6, construct a 99% Confidence Interval.In order to use technology, you need to compute the number of successes:x = n*p^Give your answers to three decimals.
If n = 390 and p^ (p-hat) = 0.8, construct a 99% Confidence Interval.In order to use technology, you need to compute the number of successes:x = n • p^Give your answers to three decimals.? < p < ?
If n = 200 and �^ (p-hat) = 0.65, construct a 95% confidence interval.Give your answers to three decimals
If n=440 and ˆpp^ (p-hat) = 0.08, construct a 99% confidence interval.
How can I find the 95% confidence interval for a hazard ratio based on theta1 and theta2 from an exponential distribution? Please can you give an example?
If n=110 and �^ (p-hat) =0.3, find the margin of error at a 90% confidence levelGive your answer to three decimals
If n = 100 and �^ (p-hat) = 0.75, construct a 99% confidence interval.Give your answers to three decimals < p <
Question 5 > We wish to estimate what percent of adult residents in a certain county are parents. Out of 200 adult residents sampled, 184 had kids. Based on this, construct a 99% confidence interval for the proportionp of adult residents who are parents in this county. Express your answer in tri-inequality form. Give your answers as decimals, to three places. < p < Express the same answer using the point estimate and margin of error. Give your answers as decimals, to three places. p = Submit Question
If n=190 and ˆpp^ (p-hat) = 0.95, construct a 99% confidence interval.Give your answers to three decimals.
If n = 560 and p^ (p-hat) = 0.45, construct a 95% confidence interval.
If n= 340 and p^ ( p-hat)= 0.05, construct a 90% confidence interval. Give your answers to three decimals
If n = 320 and ˆpp^ (p-hat) = 0.55, construct a 95% confidence interval.Give your answers to three decimals