Olivia attends school at the University of Alberta and decides to compile a contingency table of students who are taking various degrees. She surveys a group of students, and the data she collects is listed in the contingency table below. Olivia want to see if degree and gender are dependent variables. PhD Masters Undergraduate -----+--+--------+- :Male : 19 : 21 -----+--+----- :Female 13: (a) In performing this statistical test, state the hypotheses. O Ho: Degree and gender are dependent vs. HA: Degree and gender are independent O Họ: Degree is associated with gender vs. Ha: Degree is not associated with gender O Ho: The proportion of female students is the same as the proportion of male students vs. Ha: The proportion of female students is not the same as the proportion of male students O Họ: Degree is related to gender vs. Ha: Degree is not related to gender O Ho: Degree and gender are independent vs. Ha: Degree and gender are dependent (b) What is the expected frequencies of each cell? Fill out the table. (Round your answers to 2 decimal places, if needed.) PhD Masters Undergraduate Male 16.88 Female 66.15 (c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS = (d) The test statistic follows a chi-square distribution with df = 6 (e) Using the statistical table, the p-value is 0< p-value < 0.005 (f) Based on the p-value, those conducting the test should fail to reject + the null hypothesis at the significance level of 0.01. (g) What is the appropriate conclusion? O There is sufficient evidence to conclude degree and gender are independent. O There is sufficient evidence to conclude the proportion of females is not the same for each degree. O There is insufficient evidence to conclude degree and gender are independent O There is insufficient evidence to conclude degree and gender are dependent. O There is sufficient evidence to conclude degree and gender are dependent.
Olivia attends school at the University of Alberta and decides to compile a contingency table of students who are taking various degrees. She surveys a group of students, and the data she collects is listed in the contingency table below. Olivia want to see if degree and gender are dependent variables. PhD Masters Undergraduate -----+--+--------+- :Male : 19 : 21 -----+--+----- :Female 13: (a) In performing this statistical test, state the hypotheses. O Ho: Degree and gender are dependent vs. HA: Degree and gender are independent O Họ: Degree is associated with gender vs. Ha: Degree is not associated with gender O Ho: The proportion of female students is the same as the proportion of male students vs. Ha: The proportion of female students is not the same as the proportion of male students O Họ: Degree is related to gender vs. Ha: Degree is not related to gender O Ho: Degree and gender are independent vs. Ha: Degree and gender are dependent (b) What is the expected frequencies of each cell? Fill out the table. (Round your answers to 2 decimal places, if needed.) PhD Masters Undergraduate Male 16.88 Female 66.15 (c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS = (d) The test statistic follows a chi-square distribution with df = 6 (e) Using the statistical table, the p-value is 0< p-value < 0.005 (f) Based on the p-value, those conducting the test should fail to reject + the null hypothesis at the significance level of 0.01. (g) What is the appropriate conclusion? O There is sufficient evidence to conclude degree and gender are independent. O There is sufficient evidence to conclude the proportion of females is not the same for each degree. O There is insufficient evidence to conclude degree and gender are independent O There is insufficient evidence to conclude degree and gender are dependent. O There is sufficient evidence to conclude degree and gender are dependent.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![Olivia attends school at the University of Alberta and decides to compile a contingency table of students who are taking various degrees. She surveys a group of students, and the data she collects is listed in the contingency table below. Olivia wants to see if degree and gender are dependent variables.
| | PhD | Masters | Undergraduate |
|-------|-----|---------|---------------|
| Male | 19 | 21 | 75 |
| Female| 13 | 25 | 65 |
(a) In performing this statistical test, state the hypotheses.
- \(H_0\): Degree and gender are dependent vs. \(H_a\): Degree and gender are independent
- ⭕ \(H_0\): Degree is associated with gender vs. \(H_a\): Degree is not associated with gender
- ⭕ \(H_0\): The proportion of female students is the same as the proportion of male students vs. \(H_a\): The proportion of female students is not the same as the proportion of male students
- ⭕ \(H_0\): Degree is related to gender vs. \(H_a\): Degree is not related to gender
- ⭕ \(H_0\): Degree and gender are independent vs. \(H_a\): Degree and gender are dependent
(b) What is the expected frequencies of each cell? Fill out the table. (Round your answers to 2 decimal places, if needed.)
| | PhD | Masters | Undergraduate |
|-------|------|---------|---------------|
| Male | 16.88| | 75 |
| Female| | | 66.15 |
(c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.)
\[ TS = \underset{\phantom{x}}{\_} \]
(d) The test statistic follows a \(\chi\)-square distribution with \(df = 6\).
(e) Using the statistical table, the p-value is \(0 < p\text{-value} < 0.005\).
(f) Based on the p-value, those conducting the test should ___ fail to reject ___ the null hypothesis at the significance level of 0.01.
(g) What is the appropriate conclusion?
- ⭕ There is sufficient evidence to conclude degree and gender are independent.
- ⭕ There is sufficient](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F650192d1-d2bd-4507-bb57-c42486ecf22d%2F147f8a37-82c2-4be2-9df6-4b5d2cc2a027%2F3bvwis_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Olivia attends school at the University of Alberta and decides to compile a contingency table of students who are taking various degrees. She surveys a group of students, and the data she collects is listed in the contingency table below. Olivia wants to see if degree and gender are dependent variables.
| | PhD | Masters | Undergraduate |
|-------|-----|---------|---------------|
| Male | 19 | 21 | 75 |
| Female| 13 | 25 | 65 |
(a) In performing this statistical test, state the hypotheses.
- \(H_0\): Degree and gender are dependent vs. \(H_a\): Degree and gender are independent
- ⭕ \(H_0\): Degree is associated with gender vs. \(H_a\): Degree is not associated with gender
- ⭕ \(H_0\): The proportion of female students is the same as the proportion of male students vs. \(H_a\): The proportion of female students is not the same as the proportion of male students
- ⭕ \(H_0\): Degree is related to gender vs. \(H_a\): Degree is not related to gender
- ⭕ \(H_0\): Degree and gender are independent vs. \(H_a\): Degree and gender are dependent
(b) What is the expected frequencies of each cell? Fill out the table. (Round your answers to 2 decimal places, if needed.)
| | PhD | Masters | Undergraduate |
|-------|------|---------|---------------|
| Male | 16.88| | 75 |
| Female| | | 66.15 |
(c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.)
\[ TS = \underset{\phantom{x}}{\_} \]
(d) The test statistic follows a \(\chi\)-square distribution with \(df = 6\).
(e) Using the statistical table, the p-value is \(0 < p\text{-value} < 0.005\).
(f) Based on the p-value, those conducting the test should ___ fail to reject ___ the null hypothesis at the significance level of 0.01.
(g) What is the appropriate conclusion?
- ⭕ There is sufficient evidence to conclude degree and gender are independent.
- ⭕ There is sufficient
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