Hello,  can you help me with this math problem and show me step by step to understand this math problem. Thank you.In a random sample of 8, people the mean commute time to work was 36.5 mins and the standard deviation was 7.4 mins . A 98% confidence interval using the t-distribution was calculated (2.87, 44.3). After researching commute times to work, it was found that the population standard deviation is 8.8 mins. Find the margin of error and construct a 98% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.The margin of error of μ is________(Round to two decimal places as​ needed.)

Question
Asked Mar 29, 2019
36 views

Hello,  can you help me with this math problem and show me step by step to understand this math problem. Thank you.

In a random sample of 8, people the mean commute time to work was 36.5 mins and the standard deviation was 7.4 mins . A 98% confidence interval using the t-distribution was calculated (2.87, 44.3). After researching commute times to work, it was found that the population standard deviation is 8.8 mins. Find the margin of error and construct a 98% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.

The margin of error of μ is________

(Round to two decimal places as​ needed.)

 

check_circle

Expert Answer

Step 1

The provided values are:

fullscreen
Step 2

Here, the population standard deviation is known. So, we use the standard normal distribution.

The formula to calculate the confidence interval for the population mean is:

fullscreen
Step 3

The critical value at 98% confidence lev...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Hypothesis Testing

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Jane has stored three albums on her iPod. The first album consists of 11 songs by Frank Sinatra, the...

A: According to the given question, Jane has stored three albums on her iPod.The first album consists o...

question_answer

Q: Hi. How do you calculate this Poisson Distribution in the TI-83? Thanks.

A: Let ‘Y’ be the waiting time between two busses which follows exponential distribution with mean wait...

question_answer

Q: In a survey of 4061 ​adults, 738 say they have seen a ghost. Construct a​ 99% confidence interval fo...

A: In this question, it has been given that 738 people out of 4061 people have seen the ghost, we have ...

question_answer

Q: Describe the main difference between a dependent and an independent t test. (Note: I am not asking y...

A: Dependent t-test: The dependent t-test, also known as the “paired t-test”, is a statistical procedur...

question_answer

Q: Natasha is a physician looking to determine whether a supplement is effective in helping men lose we...

A: According to the given question, Natasha is a physician looking to determine whether a supplement is...

question_answer

Q: A researcher wants to test to see if husbands are significantly older than their wives. To do this, ...

A: The aim is to find the accurate statement from the following options to evaluate the population mean...

question_answer

Q: Phil Dunphy, a real estate agent, is considering whether he should list an unusual $345,507 house fo...

A: Profit received by the agent if he sells the house = (Commission received – amount spent on advertis...

question_answer

Q: About 42.3% of Californians and 19.6% of all Americans over age five speak a language other than Eng...

A: Solution:Let us consider that your class has 30 students.Null and alternative hypotheses:Here, to ch...

question_answer

Q: A test consists of 940 true or false questions. If the student guesses on each​ question, what is th...

A: Given number of true or false questions = n = 940.Probability of correct answer p = 1/2Here we can s...