A professor in the psychology department would like to determine whether there has been a significant change in grading practices over the years. It is known that the overall grade distribution for the department in 1985 had 14% A's, 26% B's, 31% C's, 19% D's, and 10% F's. A sample of n = 200 psychology students from last semester produced the following grade distribution: A 32% 11% 14% 31% 12% Do the data indicate a significant change in the grade distribution? Test at the .05 level of significance. Use Chi-square.
A professor in the psychology department would like to determine whether there has been a significant change in grading practices over the years. It is known that the overall grade distribution for the department in 1985 had 14% A's, 26% B's, 31% C's, 19% D's, and 10% F's. A sample of n = 200 psychology students from last semester produced the following grade distribution: A 32% 11% 14% 31% 12% Do the data indicate a significant change in the grade distribution? Test at the .05 level of significance. Use Chi-square.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Do the data indicate a significant change in grade distribution? Test at the .05 level of significance. Use Chi-square
![**Question 1: Chi-Square Test and Analysis**
**Formulas for Chi-Square:**
The Chi-square statistic is calculated using the formula:
\[
\chi^2 = \sum \frac{(f_{observed} - f_{expected})^2}{f_{expected}}
\]
- **\(f_{observed}\):** Frequency that is observed in the experiment.
- **\(f_{expected}\):** Theoretical frequency.
**Effect Size for Chi-Square (Applicable for 2x2 contingency table):**
\[
\varphi = \sqrt{\frac{\chi^2}{N}}
\]
- **\(\chi^2\):** Chi-square calculated for the sample.
- **\(N\):** Number of observations in the sample.
---
A professor in the psychology department seeks to determine whether grading practices have significantly changed over the years. Historically, in 1985, the grade distributions were:
- 14% A's
- 26% B's
- 31% C's
- 19% D's
- 10% F's
A sample of \( n = 200 \) psychology students from the last semester revealed the following grade distribution:
- **A:** 32%
- **B:** 11%
- **C:** 14%
- **D:** 31%
- **F:** 12%
**Question:** Do the data indicate a significant change in the grade distribution? Test this at the 0.05 level of significance using the Chi-square test.
**Instructions:**
1. Calculate the expected frequencies based on 1985's distributions.
2. Compute \( \chi^2 \) using the observed and expected frequencies.
3. Compare the calculated \( \chi^2 \) value against the critical value from the Chi-square distribution table for the appropriate degrees of freedom.
4. Determine significance and effect size as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2c28418-a35a-446b-a108-7c356c7aba50%2F0c69698a-50c8-4fb1-9ebf-4875f875cce6%2F38pm36r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 1: Chi-Square Test and Analysis**
**Formulas for Chi-Square:**
The Chi-square statistic is calculated using the formula:
\[
\chi^2 = \sum \frac{(f_{observed} - f_{expected})^2}{f_{expected}}
\]
- **\(f_{observed}\):** Frequency that is observed in the experiment.
- **\(f_{expected}\):** Theoretical frequency.
**Effect Size for Chi-Square (Applicable for 2x2 contingency table):**
\[
\varphi = \sqrt{\frac{\chi^2}{N}}
\]
- **\(\chi^2\):** Chi-square calculated for the sample.
- **\(N\):** Number of observations in the sample.
---
A professor in the psychology department seeks to determine whether grading practices have significantly changed over the years. Historically, in 1985, the grade distributions were:
- 14% A's
- 26% B's
- 31% C's
- 19% D's
- 10% F's
A sample of \( n = 200 \) psychology students from the last semester revealed the following grade distribution:
- **A:** 32%
- **B:** 11%
- **C:** 14%
- **D:** 31%
- **F:** 12%
**Question:** Do the data indicate a significant change in the grade distribution? Test this at the 0.05 level of significance using the Chi-square test.
**Instructions:**
1. Calculate the expected frequencies based on 1985's distributions.
2. Compute \( \chi^2 \) using the observed and expected frequencies.
3. Compare the calculated \( \chi^2 \) value against the critical value from the Chi-square distribution table for the appropriate degrees of freedom.
4. Determine significance and effect size as needed.
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