Question

We use the $t$ distribution to construct a confidence interval for the population mean when the underlying population standard deviation is not known. Under the assumption that the population is normally distributed, find $t_{a/2, df}$ for the following scenarios. (You may find it useful to reference the $t$ table. Round your answers to 3 decimal places.) a. A 90% confidence level and a sample of 13 observations. b. A 95% confidence level and a sample of 13 observations. c. A 90% confidence level and a sample of 22 observations. d. A 95% confidence level and a sample of 22 observations.

          We use the $t$ distribution to construct a confidence interval for the population mean when the underlying population standard deviation
is not known. Under the assumption that the population is normally distributed, find $t_{a/2, df}$ for the following scenarios. (You may find
it useful to reference the $t$ table. Round your answers to 3 decimal places.)
a. A 90% confidence level and a sample of 13 observations.
b. A 95% confidence level and a sample of 13 observations.
c. A 90% confidence level and a sample of 22 observations.
d. A 95% confidence level and a sample of 22 observations.
        
Show more…
We use the t distribution to construct a confidence interval for the population mean when the underlying population standard deviation
is not known. Under the assumption that the population is normally distributed, find ta/2, df for the following scenarios. (You may find
it useful to reference the t table. Round your answers to 3 decimal places.)
a. A 90% confidence level and a sample of 13 observations.
b. A 95% confidence level and a sample of 13 observations.
c. A 90% confidence level and a sample of 22 observations.
d. A 95% confidence level and a sample of 22 observations.

Added by Katherine W.

Close

Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
it useful to reference the t toble.Round your enswers to 3 decimal places.) A90% confidence level and a sample of 13 observations A95% confidence level and a sample of 13 observations A90% confidence lovel and a sample of 22 observations A.95% confidence level and a sample of 22 observations
Close icon
Play audio
Feedback
Powered by NumerAI
David Collins Ivan Kochetkov
Kathleen Carty verified

James Kiss and 91 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
we-use-the-t-distribution-to-construct-a-confidence-interval-for-the-population-mean-when-the-underlying-population-standard-deviation-is-not-knownunder-the-assumption-that-the-population-is-55643

James K.

we-use-the-t-distribution-to-construct-a-confidence-interval-for-the-population-mean-when-the-underlying-population-standard-deviation-is-not-knownunder-the-assumption-that-the-population-is-40548

Keondre P.

if-n13-t-44-and-514-construct-confidence-interval-at-80-confidence-level-assume-the-data-came-from-normally-distributed-population_-round-z-values-to-2-decimals_-and-round-t-values-to-3-deci-73246

If n=13, x̄=44, and s=14, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population. Round z-values to 2 decimals, and round t-values to 3 decimals. Give your final answers to one decimal place. Select an answer

Hoan N.


*

Recommended Textbooks

-
Elementary Statistics a Step by Step Approach

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition
achievement 1,223 solutions
The Practice of Statistics for AP

The Practice of Statistics for AP

Daren S. Starnes, Daniel S. Yates, David S. Moore 4th Edition
achievement 1,870 solutions
Introductory Statistics

Introductory Statistics

Barbara Illowsky, Susan Dean 1st Edition
achievement 1,135 solutions

*

Transcript

-
00:01 To find the t value for a given confidence level in sample size, we need to determine the degrees of freedom and then consult the t distribution table or use a calculator.
00:13 For a 99 % confidence level in a sample of 12 observations, the degrees of freedom is equal to n minus one, which would be 12 minus one or 11.
00:21 And looking up in the t distribution table for a 99 % confidence level with 11 degrees of freedom, the t value is about 3 .106.
00:40 For a 90 % confidence level in a sample of 12 observations, the degrees of freedom is again 11.
00:47 And consulting that t distribution table for a 90 % confidence level with 11 degrees of freedom, the t value is approximately 1 .796...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade


Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever