An examination in biology has been taken by biology majors and also by some students from other majors. It is widely believed that the scores for both groups are normally distributed. A random sample of 27 examinations completed by biology majors and an independent random sample of 16 examinations completed by students from other majors are selected. Among sampled students, the biology majors scored a mean of 536.5 points with a variance of 10,920.25 , and the students from other majors scored a mean of 493.3 points with a variance of 28,493.44 . Can we conclude, at the 0.01 significance level, that the population variance of scores of biology majors, of, is less than o, the population variance of scores of other majors? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ħ, and the alternative hypothesis #,. Ho : 0 H1 : 0 |(b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) D=0 OsO ? (d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.) (e) Can we conclude that the variance of all scores of biology majors is less than the variance of all scores of other majors? Yes No
An examination in biology has been taken by biology majors and also by some students from other majors. It is widely believed that the scores for both groups are normally distributed. A random sample of 27 examinations completed by biology majors and an independent random sample of 16 examinations completed by students from other majors are selected. Among sampled students, the biology majors scored a mean of 536.5 points with a variance of 10,920.25 , and the students from other majors scored a mean of 493.3 points with a variance of 28,493.44 . Can we conclude, at the 0.01 significance level, that the population variance of scores of biology majors, of, is less than o, the population variance of scores of other majors? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ħ, and the alternative hypothesis #,. Ho : 0 H1 : 0 |(b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) D=0 OsO ? (d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.) (e) Can we conclude that the variance of all scores of biology majors is less than the variance of all scores of other majors? Yes No
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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![**Educational Website Transcription:**
**Title: Significance Testing in Biology Exam Scores**
An examination in biology has been taken by biology majors and also by some students from other majors. It is widely believed that the scores for both groups are normally distributed.
A random sample of 27 examinations completed by biology majors and an independent random sample of 16 examinations completed by students from other majors are selected. Among sampled students, the biology majors scored a mean of 536.5 points with a variance of 10,920.25, and the students from other majors scored a mean of 493.3 points with a variance of 28,493.44.
Can we conclude, at the 0.01 significance level, that the population variance of scores of biology majors, \(\sigma^2_1\), is less than \(\sigma^2_2\), the population variance of scores of other majors?
**Objective: Perform a one-tailed test.**
**Instructions:** Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.)
---
**Steps:**
(a) **State the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\):**
- \(H_0: [ ]\)
- \(H_1: [ ]\)
(b) **Determine the type of test statistic to use:**
*(Choose one from the dropdown list.)*
(c) **Find the value of the test statistic:**
*(Round to three or more decimal places.)*
\([ ]\)
(d) **Find the critical value at the 0.01 level of significance:**
*(Round to three or more decimal places.)*
\([ ]\)
(e) **Conclusion:**
Can we conclude that the variance of all scores of biology majors is less than the variance of all scores of other majors?
- Yes
- No
---
**Diagram Explanation:**
On the right side, there is a key for statistical symbols:
- \(\mu\) represents population mean.
- \(\sigma\) represents population standard deviation.
- \(p\) is the population proportion.
- \(\bar{x}\) is the sample mean.
- \(s\) is the sample standard deviation.
- \(\hat{p}\) represents sample proportion](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febcf9de3-24cc-40b0-a023-15a9096e4963%2Fb8233bc6-4b76-43ba-98c2-ff8bab5b8a78%2Fygrerl_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Website Transcription:**
**Title: Significance Testing in Biology Exam Scores**
An examination in biology has been taken by biology majors and also by some students from other majors. It is widely believed that the scores for both groups are normally distributed.
A random sample of 27 examinations completed by biology majors and an independent random sample of 16 examinations completed by students from other majors are selected. Among sampled students, the biology majors scored a mean of 536.5 points with a variance of 10,920.25, and the students from other majors scored a mean of 493.3 points with a variance of 28,493.44.
Can we conclude, at the 0.01 significance level, that the population variance of scores of biology majors, \(\sigma^2_1\), is less than \(\sigma^2_2\), the population variance of scores of other majors?
**Objective: Perform a one-tailed test.**
**Instructions:** Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.)
---
**Steps:**
(a) **State the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\):**
- \(H_0: [ ]\)
- \(H_1: [ ]\)
(b) **Determine the type of test statistic to use:**
*(Choose one from the dropdown list.)*
(c) **Find the value of the test statistic:**
*(Round to three or more decimal places.)*
\([ ]\)
(d) **Find the critical value at the 0.01 level of significance:**
*(Round to three or more decimal places.)*
\([ ]\)
(e) **Conclusion:**
Can we conclude that the variance of all scores of biology majors is less than the variance of all scores of other majors?
- Yes
- No
---
**Diagram Explanation:**
On the right side, there is a key for statistical symbols:
- \(\mu\) represents population mean.
- \(\sigma\) represents population standard deviation.
- \(p\) is the population proportion.
- \(\bar{x}\) is the sample mean.
- \(s\) is the sample standard deviation.
- \(\hat{p}\) represents sample proportion
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