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The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts (a) and (b) below, X3 51 X2 44 (35.39)(44.42(47.1 19 20 17 (15.61)(19 58)(20.1 32 (a) Compute the value of the chi-square test statistic. Y= 2,079 (Round to three decimal places as needed.) (b) Test the hypothesis that X and Y are independent at the a = 0.01 level of significance. VA. H: The Y category andX category are independent. H,: The Y category and X category are dependent.

The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts (a) and (b) below, X3 51 X2 44 (35.39)(44.42(47.1 19 20 17 (15.61)(19 58)(20.1 32 (a) Compute the value of the chi-square test statistic. Y= 2,079 (Round to three decimal places as needed.) (b) Test the hypothesis that X and Y are independent at the a = 0.01 level of significance. VA. H: The Y category andX category are independent. H,: The Y category and X category are dependent.

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
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**Chi-Square Test Analysis** This section examines a table of observed and expected values for two categorical variables, X and Y. Variable X has three categories (X₁, X₂, X₃), and variable Y has two categories (Y₁, Y₂). The observed and expected values are used to perform a chi-square test. **Data Table:** - **Category Y₁:** - X₁: Observed = 32, Expected = 35.39 - X₂: Observed = 44, Expected = 44.42 - X₃: Observed = 51, Expected = 47.19 - **Category Y₂:** - X₁: Observed = 19, Expected = 15.61 - X₂: Observed = 20, Expected = 19.58 - X₃: Observed = 17, Expected = 20.81 **Tasks:** (a) **Compute the Value of the Chi-Square Test Statistic:** - The calculated chi-square test statistic is 2.079. (Note: Results are rounded to three decimal places as needed.) (b) **Hypothesis Testing at α = 0.01 Level of Significance:** - **Option A:** - **H₀:** The Y category and X category are independent. - **H₁:** The Y category and X category are dependent. - **Option B:** - **H₀:** The Y category and X category have equal proportions. - **H₁:** The proportions are not equal. **Instructions:** Enter your answer in the answer box and then click "Check Answer" to see if your hypothesis test results are correct.
Transcribed Image Text:**Chi-Square Test Analysis** This section examines a table of observed and expected values for two categorical variables, X and Y. Variable X has three categories (X₁, X₂, X₃), and variable Y has two categories (Y₁, Y₂). The observed and expected values are used to perform a chi-square test. **Data Table:** - **Category Y₁:** - X₁: Observed = 32, Expected = 35.39 - X₂: Observed = 44, Expected = 44.42 - X₃: Observed = 51, Expected = 47.19 - **Category Y₂:** - X₁: Observed = 19, Expected = 15.61 - X₂: Observed = 20, Expected = 19.58 - X₃: Observed = 17, Expected = 20.81 **Tasks:** (a) **Compute the Value of the Chi-Square Test Statistic:** - The calculated chi-square test statistic is 2.079. (Note: Results are rounded to three decimal places as needed.) (b) **Hypothesis Testing at α = 0.01 Level of Significance:** - **Option A:** - **H₀:** The Y category and X category are independent. - **H₁:** The Y category and X category are dependent. - **Option B:** - **H₀:** The Y category and X category have equal proportions. - **H₁:** The proportions are not equal. **Instructions:** Enter your answer in the answer box and then click "Check Answer" to see if your hypothesis test results are correct.
**Hypothesis Testing and Contingency Tables** This exercise involves analyzing a contingency table to evaluate the relationship between two categorical variables, X and Y. The table presents observed and expected values for these variables, helping us to complete the following statistical hypotheses: ### Hypotheses Options: - **A:** - \( H_0 \): The \( y \) category and \( x \) category are independent. - \( H_1 \): The \( y \) category and \( x \) category are not independent. - **B:** - \( H_0 \): The \( y \) category and \( x \) category have equal proportions. - \( H_1 \): The proportions are not equal. - **C:** - \( H_0 \): The \( y \) category and \( x \) category are independent. - \( H_1 \): The \( y \) category and \( x \) category are not independent. - **D:** - \( H_0: \mu_k = E_k \) - \( H_1: \mu_k \neq E_k \) or \( \mu_k > E_k \) ### Question: What is the P-value? (Round to three decimal places as needed.) ### Contingency Table Analysis: The table displays observed and expected frequencies for two variables, X (with three categories: \( X_1, X_2, X_3 \)) and Y (with two categories: \( Y_1, Y_2 \)). | | \( X_1 \) | \( X_2 \) | \( X_3 \) | |----|-----------|-----------|-----------| | \( Y_1 \) | 32 (33.50) | 44 (44.42) | 51 (47.16) | | \( Y_2 \) | 19 (15.50) | 20 (19.58) | 17 (20.84) | - **Observed Values:** Represent the actual collected data within each category combination of X and Y. - **Expected Values (in parentheses):** These are the frequencies expected under the null hypothesis of independence. Use the differences between observed and expected values to compute the appropriate statistical tests and ultimately calculate the P-value.
Transcribed Image Text:**Hypothesis Testing and Contingency Tables** This exercise involves analyzing a contingency table to evaluate the relationship between two categorical variables, X and Y. The table presents observed and expected values for these variables, helping us to complete the following statistical hypotheses: ### Hypotheses Options: - **A:** - \( H_0 \): The \( y \) category and \( x \) category are independent. - \( H_1 \): The \( y \) category and \( x \) category are not independent. - **B:** - \( H_0 \): The \( y \) category and \( x \) category have equal proportions. - \( H_1 \): The proportions are not equal. - **C:** - \( H_0 \): The \( y \) category and \( x \) category are independent. - \( H_1 \): The \( y \) category and \( x \) category are not independent. - **D:** - \( H_0: \mu_k = E_k \) - \( H_1: \mu_k \neq E_k \) or \( \mu_k > E_k \) ### Question: What is the P-value? (Round to three decimal places as needed.) ### Contingency Table Analysis: The table displays observed and expected frequencies for two variables, X (with three categories: \( X_1, X_2, X_3 \)) and Y (with two categories: \( Y_1, Y_2 \)). | | \( X_1 \) | \( X_2 \) | \( X_3 \) | |----|-----------|-----------|-----------| | \( Y_1 \) | 32 (33.50) | 44 (44.42) | 51 (47.16) | | \( Y_2 \) | 19 (15.50) | 20 (19.58) | 17 (20.84) | - **Observed Values:** Represent the actual collected data within each category combination of X and Y. - **Expected Values (in parentheses):** These are the frequencies expected under the null hypothesis of independence. Use the differences between observed and expected values to compute the appropriate statistical tests and ultimately calculate the P-value.
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