Expected Frequency Frequency Observed Blood Type Residual 44 A 12 В 23 AB 5 Н. : РА — 0.6; рв — 0.2; рс — 0.15; pp 3D 0.05 H1: at least one is different Driginal claim = Select an answer Enter the critical value, along with the significance level and degrees of freedom x(a.dn below the graph. (Graph is for illustration only. No need to shade.) X2- Distribution 0.12 0.1 0.08 0.06 0.04 0.02 93a 华号5以印乃乃的组印 17 (Round to three decimal places.) Test Statistic = (Round to three decimal places.) p-value= (Round to four decimal places.) Decision: [ Select an answer Conclusion: Select an answer blood type is different for millionaires. A the claim that the distribution of Probability 103 60T 115 121 127 133 139

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### Blood Type Distribution in Millionaires: Chi-Square Test

In the US, 60% of all people have type O blood, 20% have type A blood, 15% have type B blood and 5% have type AB blood. A researcher wants to see if the distribution of blood type is different for millionaires. The table below shows the results of a random sample of 84 millionaires. What can be concluded at the 0.1% significant level. Test for the claim that the following categories occur with the following frequencies: \( p_{\text{Type O}} = 0.6 \); \( p_{\text{Type A}} = 0.2 \); \( p_{\text{Type B}} = 0.15 \); \( p_{\text{Type AB}} = 0.05 \). Test at the 0.1 significance level. Complete the table. Round all answers to three decimal places.

| Blood Type | Observed Frequency | Expected Frequency | Residual |
|------------|--------------------|--------------------|----------|
| O          | 44                 |                    |          |
| A          | 12                 |                    |          |
| B          | 23                 |                    |          |
| AB         | 5                  |                    |          |

\[ H_0: p_A = 0.6; \quad p_B = 0.2; \quad p_C = 0.15; \quad p_D = 0.05 \]
\[ H_1: \text{at least one is different} \]

**Original claim:**
\[ \text{Enter an answer} \]

Enter the critical value, along with the significance level and degrees of freedom \( \chi^2 (\alpha, df) \) below the graph. (Graph is for illustration only. No need to shade.)

**Graph Description:**
The graph displays the Chi-Square (\( \chi^2 \)) distribution with varying probabilities on the y-axis and the Chi-Square values on the x-axis. The graph is unimodal, skewed to the right, typical of a Chi-Square distribution.

\[ X^2 \text{ Distribution} \]

| \( X \)   | 1  | 17 | 33 | 49 | 65 | 81 | 97 | 113 | 129 |
|-----------|----|----|----|----
Transcribed Image Text:### Blood Type Distribution in Millionaires: Chi-Square Test In the US, 60% of all people have type O blood, 20% have type A blood, 15% have type B blood and 5% have type AB blood. A researcher wants to see if the distribution of blood type is different for millionaires. The table below shows the results of a random sample of 84 millionaires. What can be concluded at the 0.1% significant level. Test for the claim that the following categories occur with the following frequencies: \( p_{\text{Type O}} = 0.6 \); \( p_{\text{Type A}} = 0.2 \); \( p_{\text{Type B}} = 0.15 \); \( p_{\text{Type AB}} = 0.05 \). Test at the 0.1 significance level. Complete the table. Round all answers to three decimal places. | Blood Type | Observed Frequency | Expected Frequency | Residual | |------------|--------------------|--------------------|----------| | O | 44 | | | | A | 12 | | | | B | 23 | | | | AB | 5 | | | \[ H_0: p_A = 0.6; \quad p_B = 0.2; \quad p_C = 0.15; \quad p_D = 0.05 \] \[ H_1: \text{at least one is different} \] **Original claim:** \[ \text{Enter an answer} \] Enter the critical value, along with the significance level and degrees of freedom \( \chi^2 (\alpha, df) \) below the graph. (Graph is for illustration only. No need to shade.) **Graph Description:** The graph displays the Chi-Square (\( \chi^2 \)) distribution with varying probabilities on the y-axis and the Chi-Square values on the x-axis. The graph is unimodal, skewed to the right, typical of a Chi-Square distribution. \[ X^2 \text{ Distribution} \] | \( X \) | 1 | 17 | 33 | 49 | 65 | 81 | 97 | 113 | 129 | |-----------|----|----|----|----
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