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A statistics teacher claims that, on average, 20% of students in his class get an A, 25% get a B, 35% get a C, 10% get a D and the rest get an F. The grades of a random sample of his students over the years is recorded. Test the claim at 10% significance. Round to the fourth as needed. Observed Categories Frequency A OF B C D F Test Statistic: 12.008 Degrees of Freedom: 4 p-val: 0.01729 53 36 80 15 27 Decision Rule: Reject the Null Expected Frequency 92.2 52.75 73.85 21.1 21.1 8 OB B 0° > ४ > 8 Did something significant happen? Significance Happened

A statistics teacher claims that, on average, 20% of students in his class get an A, 25% get a B, 35% get a C, 10% get a D and the rest get an F. The grades of a random sample of his students over the years is recorded. Test the claim at 10% significance. Round to the fourth as needed. Observed Categories Frequency A OF B C D F Test Statistic: 12.008 Degrees of Freedom: 4 p-val: 0.01729 53 36 80 15 27 Decision Rule: Reject the Null Expected Frequency 92.2 52.75 73.85 21.1 21.1 8 OB B 0° > ४ > 8 Did something significant happen? Significance Happened

MATLAB: An Introduction with Applications
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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The claim to be tested is that, on average, the distribution of grades in a statistics class follows the pattern where 20% of students receive an A, 25% receive a B, 35% receive a C, 10% receive a D, and the remaining 10% receive an F. A random sample of grades from the teacher's students over the years is given, and a chi-square test of significance is used to test this claim at the 10% significance level. Below are the observed and expected frequencies: | Categories | Observed Frequency | Expected Frequency | |------------|---------------------|---------------------| | A | 53 | 92.2 | | B | 36 | 52.75 | | C | 80 | 73.85 | | D | 15 | 21.1 | | F | 27 | 21.1 | **Test Calculation Details:** - **Test Statistic (Chi-Square Value):** 12.008 - **Degrees of Freedom:** 4 - **P-value:** 0.01729 **Decision Rule:** At the 10% significance level (α = 0.10), if the p-value is less than the significance level, reject the null hypothesis. **Conclusion:** - Since the p-value (0.01729) is less than the significance level (0.10), we reject the null hypothesis. - Therefore, the evidence suggests that the distribution of grades in this sample is significantly different from the teacher's claimed distribution. **Notes:** - The red "x" next to "Expected Frequency" for category A indicates a large deviation from the expected value. - Green checkmarks indicate that categories B, C, D, and F closely align with their expected frequencies. This test helps to understand whether the observed distribution of grades significantly deviates from the expected distribution under the teacher's claimed probabilities.
Transcribed Image Text:The claim to be tested is that, on average, the distribution of grades in a statistics class follows the pattern where 20% of students receive an A, 25% receive a B, 35% receive a C, 10% receive a D, and the remaining 10% receive an F. A random sample of grades from the teacher's students over the years is given, and a chi-square test of significance is used to test this claim at the 10% significance level. Below are the observed and expected frequencies: | Categories | Observed Frequency | Expected Frequency | |------------|---------------------|---------------------| | A | 53 | 92.2 | | B | 36 | 52.75 | | C | 80 | 73.85 | | D | 15 | 21.1 | | F | 27 | 21.1 | **Test Calculation Details:** - **Test Statistic (Chi-Square Value):** 12.008 - **Degrees of Freedom:** 4 - **P-value:** 0.01729 **Decision Rule:** At the 10% significance level (α = 0.10), if the p-value is less than the significance level, reject the null hypothesis. **Conclusion:** - Since the p-value (0.01729) is less than the significance level (0.10), we reject the null hypothesis. - Therefore, the evidence suggests that the distribution of grades in this sample is significantly different from the teacher's claimed distribution. **Notes:** - The red "x" next to "Expected Frequency" for category A indicates a large deviation from the expected value. - Green checkmarks indicate that categories B, C, D, and F closely align with their expected frequencies. This test helps to understand whether the observed distribution of grades significantly deviates from the expected distribution under the teacher's claimed probabilities.
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