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Test the claim that births occur with the same frequency on different days of the week at the 0.01 significance level. Complete the table. Round all answers to three decimal places. Day of Week Observed Expected (0 – E)² Frequency Frequency E Sunday 9 Monday | 23 Tuesday 23

Test the claim that births occur with the same frequency on different days of the week at the 0.01 significance level. Complete the table. Round all answers to three decimal places. Day of Week Observed Expected (0 – E)² Frequency Frequency E Sunday 9 Monday | 23 Tuesday 23

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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**Chi-Square Distribution Analysis** To conduct a chi-square test, enter the critical value along with the significance level and degrees of freedom. The graph provided illustrates the chi-square (χ²) distribution. **Graph Explanation:** - **Title:** χ² - Distribution - **Axes:** - The x-axis (horizontal) represents the chi-square statistic values ranging from 0 to 139. - The y-axis (vertical) represents the probability, with values up to 0.12. - **Curve:** - The graph shows a positively skewed curve starting near 0 on the x-axis, peaking between 10 and 20, then gradually tapering off as the x-values increase. **Input Section:** - **Critical Value (χ²(α, df)):** - Significance Level (α): [Input Field] - Degrees of Freedom (df): [Input Field] - Critical Value: [Input Field] - *(Round to three decimal places.)* **Calculation Fields:** - **Test Statistic:** [Input Field] - *(Round to three decimal places.)* - **p-value:** [Input Field] - *(Round to four decimal places.)* **Decision:** - **Decision:** [Dropdown Selection] - Choose whether to reject or fail to reject the null hypothesis. **Conclusion:** - **Conclusion:** [Dropdown Selection] - Choose the appropriate conclusion regarding the claim that births occur with the same frequency on different days of the week. Ensure all values are accurately calculated and rounded as specified for precise analysis and interpretation.
Transcribed Image Text:**Chi-Square Distribution Analysis** To conduct a chi-square test, enter the critical value along with the significance level and degrees of freedom. The graph provided illustrates the chi-square (χ²) distribution. **Graph Explanation:** - **Title:** χ² - Distribution - **Axes:** - The x-axis (horizontal) represents the chi-square statistic values ranging from 0 to 139. - The y-axis (vertical) represents the probability, with values up to 0.12. - **Curve:** - The graph shows a positively skewed curve starting near 0 on the x-axis, peaking between 10 and 20, then gradually tapering off as the x-values increase. **Input Section:** - **Critical Value (χ²(α, df)):** - Significance Level (α): [Input Field] - Degrees of Freedom (df): [Input Field] - Critical Value: [Input Field] - *(Round to three decimal places.)* **Calculation Fields:** - **Test Statistic:** [Input Field] - *(Round to three decimal places.)* - **p-value:** [Input Field] - *(Round to four decimal places.)* **Decision:** - **Decision:** [Dropdown Selection] - Choose whether to reject or fail to reject the null hypothesis. **Conclusion:** - **Conclusion:** [Dropdown Selection] - Choose the appropriate conclusion regarding the claim that births occur with the same frequency on different days of the week. Ensure all values are accurately calculated and rounded as specified for precise analysis and interpretation.
**Chi-Square Test for Birth Frequency over Different Days of the Week** This exercise involves testing the claim that births occur with the same frequency on different days of the week using a chi-square test at the 0.01 significance level. The task includes completing the provided table and rounding all answers to three decimal places. **Table Overview:** - **Columns:** - **Day of Week:** Lists each day from Sunday to Saturday. - **Observed Frequency (O):** The actual number of births observed on each day. - **Expected Frequency (E):** The theoretical number of births expected if they were evenly distributed across the week. - **Chi-Square Calculation \((O - E)^2 / E\):** This is calculated for each day based on the observed and expected frequencies. - **Observed Frequencies:** - Sunday: 9 - Monday: 23 - Tuesday: 23 - Wednesday: 17 - Thursday: 9 - Friday: 13 - Saturday: 16 **Hypotheses:** - **Null Hypothesis (\(H_0\)):** Birth frequencies are the same across all days (\(p_{Sun} = p_{Mon} = p_{Tue} = p_{Wed} = p_{Thu} = p_{Fri} = p_{Sat}\)). - **Alternate Hypothesis (\(H_1\)):** At least one day has a different birth frequency. **Task:** Complete the table by calculating the expected frequencies and the chi-square values for each day. Use these computations to assess the original claim. To make decisions about the hypotheses, compare the calculated chi-square statistic to the critical value from the chi-square distribution table at the 0.01 significance level. After filling out the table and performing calculations, select the appropriate answer for the original claim based on the results of the chi-square test. This exercise provides practice in conducting hypothesis testing using the chi-square test for uniform distribution, which is applicable in fields such as healthcare, statistics, and sociological research.
Transcribed Image Text:**Chi-Square Test for Birth Frequency over Different Days of the Week** This exercise involves testing the claim that births occur with the same frequency on different days of the week using a chi-square test at the 0.01 significance level. The task includes completing the provided table and rounding all answers to three decimal places. **Table Overview:** - **Columns:** - **Day of Week:** Lists each day from Sunday to Saturday. - **Observed Frequency (O):** The actual number of births observed on each day. - **Expected Frequency (E):** The theoretical number of births expected if they were evenly distributed across the week. - **Chi-Square Calculation \((O - E)^2 / E\):** This is calculated for each day based on the observed and expected frequencies. - **Observed Frequencies:** - Sunday: 9 - Monday: 23 - Tuesday: 23 - Wednesday: 17 - Thursday: 9 - Friday: 13 - Saturday: 16 **Hypotheses:** - **Null Hypothesis (\(H_0\)):** Birth frequencies are the same across all days (\(p_{Sun} = p_{Mon} = p_{Tue} = p_{Wed} = p_{Thu} = p_{Fri} = p_{Sat}\)). - **Alternate Hypothesis (\(H_1\)):** At least one day has a different birth frequency. **Task:** Complete the table by calculating the expected frequencies and the chi-square values for each day. Use these computations to assess the original claim. To make decisions about the hypotheses, compare the calculated chi-square statistic to the critical value from the chi-square distribution table at the 0.01 significance level. After filling out the table and performing calculations, select the appropriate answer for the original claim based on the results of the chi-square test. This exercise provides practice in conducting hypothesis testing using the chi-square test for uniform distribution, which is applicable in fields such as healthcare, statistics, and sociological research.
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