Suppose you have a normally distributed population such that o? S', we find that from a random sample of size n = 15, S² = 16.09. Does our population variance seem reasonable? = 8. Using the sampling distribution of Note: We will consider our population variance reasonable if our x value falls within the interval x0.975 (df), x°0.025(df)]. 1) Find the values of the interval xo.975(df), x°0.025(df)].
Suppose you have a normally distributed population such that o? S', we find that from a random sample of size n = 15, S² = 16.09. Does our population variance seem reasonable? = 8. Using the sampling distribution of Note: We will consider our population variance reasonable if our x value falls within the interval x0.975 (df), x°0.025(df)]. 1) Find the values of the interval xo.975(df), x°0.025(df)].
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![Suppose you have a normally distributed population such that \(\sigma^2 = 8\). Using the sampling distribution of \(S^2\), we find that from a random sample of size \(n = 15\), \(S^2 = 16.09\). Does our population variance seem reasonable?
Note: We will consider our population variance reasonable if our \(\chi^2\) value falls within the interval \([\chi^2_{0.975}(df), \chi^2_{0.025}(df)]\).
1) Find the values of the interval \([\chi^2_{0.975}(df), \chi^2_{0.025}(df)]\).
\[
\chi^2_{0.975}(df) =
\]
(Round to 3 decimals.)
\[
\chi^2_{0.025}(df) =
\]
(Round to 3 decimals.)
2) Find the value of \(\chi^2\) that comes from the data you collected in the problem statement.
\[
\]
(Round to 3 decimals.)
3) Is the population variance reasonable?
- [ ] Yes
- [ ] No
No work required for Part 1 or Part 3, but recommended on Part 2.
If you do not have a table, DI Management's "Compute the inverse of the p-value for a chi-square distribution" is useful to get exact answers (to many decimals).
[Add Work]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0393b910-875a-4ed6-a578-5b5396be78bf%2F760c9b7c-4791-4a65-b503-5296e8e53316%2F8a67xz_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose you have a normally distributed population such that \(\sigma^2 = 8\). Using the sampling distribution of \(S^2\), we find that from a random sample of size \(n = 15\), \(S^2 = 16.09\). Does our population variance seem reasonable?
Note: We will consider our population variance reasonable if our \(\chi^2\) value falls within the interval \([\chi^2_{0.975}(df), \chi^2_{0.025}(df)]\).
1) Find the values of the interval \([\chi^2_{0.975}(df), \chi^2_{0.025}(df)]\).
\[
\chi^2_{0.975}(df) =
\]
(Round to 3 decimals.)
\[
\chi^2_{0.025}(df) =
\]
(Round to 3 decimals.)
2) Find the value of \(\chi^2\) that comes from the data you collected in the problem statement.
\[
\]
(Round to 3 decimals.)
3) Is the population variance reasonable?
- [ ] Yes
- [ ] No
No work required for Part 1 or Part 3, but recommended on Part 2.
If you do not have a table, DI Management's "Compute the inverse of the p-value for a chi-square distribution" is useful to get exact answers (to many decimals).
[Add Work]
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