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What are the hypotheses for this test? Ho: PP Ps= P4 P Po 0.167 HA one of these proportions is different than assumed. He gender and favorite color are independent HA gender and favorite color are dependent Ho females and males are homogeneous in their color preferences H₁: females and males are heterogeneous in their color preferences

What are the hypotheses for this test? Ho: PP Ps= P4 P Po 0.167 HA one of these proportions is different than assumed. He gender and favorite color are independent HA gender and favorite color are dependent Ho females and males are homogeneous in their color preferences H₁: females and males are heterogeneous in their color preferences

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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### Hypothesis Testing on Color Preferences #### Question 31: **What are the hypotheses for this test?** - **Option 1:** - \( H_0 \): \( p_1 = p_2 = p_3 = p_4 = p_5 = p_6 = 0.167 \) - \( H_A \): One of these proportions is different than assumed. - **Option 2:** - \( H_0 \): Gender and favorite color are independent. - \( H_A \): Gender and favorite color are dependent. - **Option 3:** - \( H_0 \): Females and males are homogeneous in their color preferences. - \( H_A \): Females and males are heterogeneous in their color preferences. #### Question 32: **What assumption(s) would we need to check?** - \( \text{all } n_i p_i > 5 \) - Equal variances - Normally distributed data - \( \text{all } E_i > 5 \) #### Question 33: **What is your decision?** - Reject \( H_0 \). - There is not enough evidence to conclude that there is a relationship between gender and favorite color. - There is enough evidence to conclude that there is a relationship between gender and favorite color. - Fail to reject \( H_0 \).
Transcribed Image Text:### Hypothesis Testing on Color Preferences #### Question 31: **What are the hypotheses for this test?** - **Option 1:** - \( H_0 \): \( p_1 = p_2 = p_3 = p_4 = p_5 = p_6 = 0.167 \) - \( H_A \): One of these proportions is different than assumed. - **Option 2:** - \( H_0 \): Gender and favorite color are independent. - \( H_A \): Gender and favorite color are dependent. - **Option 3:** - \( H_0 \): Females and males are homogeneous in their color preferences. - \( H_A \): Females and males are heterogeneous in their color preferences. #### Question 32: **What assumption(s) would we need to check?** - \( \text{all } n_i p_i > 5 \) - Equal variances - Normally distributed data - \( \text{all } E_i > 5 \) #### Question 33: **What is your decision?** - Reject \( H_0 \). - There is not enough evidence to conclude that there is a relationship between gender and favorite color. - There is enough evidence to conclude that there is a relationship between gender and favorite color. - Fail to reject \( H_0 \).
### Analysis of Gender and Favorite Car Color A researcher conducted a study to determine if there is a relationship between gender and favorite car color. The significance level for this analysis is set at \(\alpha = 0.01\). #### Contingency Table The following data shows the observed and expected counts for preferred car colors by gender: | Type of Car | Gender | Female | Male | Total | | ----------- | ------ | ------ | ---- | ----- | | **blue** | Count | 180 | 185 | 365 | | | Expected | 182.5 | 182.5 | | | **red** | Count | 210 | 175 | 385 | | | Expected | 192.5 | 192.5 | | | **yellow** | Count | 110 | 140 | 250 | | | Expected | 125 | 125 | | | **Total** | | 500 | 500 | 1000 | #### Statistical Tests The statistical analysis included the calculation of several key metrics: - **Sample Size (N):** 1000 - **Degrees of Freedom (DF):** 2 - **-Log Likelihood:** 3.4317004 - **R-Square (U):** 0.0050 #### Chi-Square Test Results A likelihood ratio test was conducted to assess the relationship between gender and favorite car color: - **Chi-Square Value:** 6.863 - **Probability (Prob>ChiSq):** 0.0323* ### Interpretation The chi-square test resulted in a p-value of 0.0323, which is greater than the significance level (\(\alpha = 0.01\)). This indicates that there is no statistically significant relationship between gender and favorite car color at the 0.01 level.
Transcribed Image Text:### Analysis of Gender and Favorite Car Color A researcher conducted a study to determine if there is a relationship between gender and favorite car color. The significance level for this analysis is set at \(\alpha = 0.01\). #### Contingency Table The following data shows the observed and expected counts for preferred car colors by gender: | Type of Car | Gender | Female | Male | Total | | ----------- | ------ | ------ | ---- | ----- | | **blue** | Count | 180 | 185 | 365 | | | Expected | 182.5 | 182.5 | | | **red** | Count | 210 | 175 | 385 | | | Expected | 192.5 | 192.5 | | | **yellow** | Count | 110 | 140 | 250 | | | Expected | 125 | 125 | | | **Total** | | 500 | 500 | 1000 | #### Statistical Tests The statistical analysis included the calculation of several key metrics: - **Sample Size (N):** 1000 - **Degrees of Freedom (DF):** 2 - **-Log Likelihood:** 3.4317004 - **R-Square (U):** 0.0050 #### Chi-Square Test Results A likelihood ratio test was conducted to assess the relationship between gender and favorite car color: - **Chi-Square Value:** 6.863 - **Probability (Prob>ChiSq):** 0.0323* ### Interpretation The chi-square test resulted in a p-value of 0.0323, which is greater than the significance level (\(\alpha = 0.01\)). This indicates that there is no statistically significant relationship between gender and favorite car color at the 0.01 level.
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