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## In the US,  44.5% of all people have type O blood,  39.3% have type A blood, 11.5% have type B blood and 4.7% 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 3356 millionaires. What can be concluded at the αα = 0.05 significance level? Complete the table by filling in the expected frequencies. Round to the nearest whole number: Frequencies of Blood Type Outcome Frequency Expected Frequency O 1506   A 1330   B 373   AB 147   What is the correct statistical test to use? Select an answer Independence Homogeneity Paired t-test Goodness-of-Fit  What are the null and alternative hypotheses? H0:H0:  The distribution of blood type for millionaires is the same as it is for Americans in general. Blood type and income are independent. The distribution of blood type for millionaires is not the same as it is for Americans in general. Blood type and income are dependent. H1:H1:  The distribution of blood type for millionaires is the same as it is for Americans in general. Blood type and income are independent. Blood type and income are dependent. The distribution of blood type for millionaires is not the same as it is for Americans in general. The degrees of freedom =  The test-statistic for this data =  (Please show your answer to three decimal places.) The p-value for this sample = (Please show your answer to four decimal places.)  The p-value is Select an answer less than (or equal to) greater than  αα  Based on this, we should Select an answer reject the null accept the null fail to reject the null  Thus, the final conclusion is… There is sufficient evidence to conclude that the distribution of blood type for millionaires is the same as it is for Americans in general. There is sufficient evidence to conclude that the distribution of blood type for millionaires is not the same as it is for Americans in general. There is insufficient evidence to conclude that blood type and income are dependent. There is sufficient evidence to conclude that blood type and income are dependent. There is insufficient evidence to conclude that the distribution of blood type for millionaires is not the same as it is for Americans in general.

In the US,  44.5% of all people have type O blood,  39.3% have type A blood, 11.5% have type B blood and 4.7% 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 3356 millionaires. What can be concluded at the αα = 0.05 significance level?

1. Complete the table by filling in the expected frequencies. Round to the nearest whole number:
Frequencies of Blood Type
Outcome Frequency Expected Frequency
O 1506

A 1330
B 373
AB 147
2. What is the correct statistical test to use?
Select an answer Independence Homogeneity Paired t-test Goodness-of-Fit
3. What are the null and alternative hypotheses?
H0:H0:
• The distribution of blood type for millionaires is the same as it is for Americans in general.
• Blood type and income are independent.
• The distribution of blood type for millionaires is not the same as it is for Americans in general.
• Blood type and income are dependent.

H1:H1:

• The distribution of blood type for millionaires is the same as it is for Americans in general.
• Blood type and income are independent.
• Blood type and income are dependent.
• The distribution of blood type for millionaires is not the same as it is for Americans in general.
4. The degrees of freedom =

7. The p-value is Select an answer less than (or equal to) greater than  αα

8. Based on this, we should Select an answer reject the null accept the null fail to reject the null

9. Thus, the final conclusion is…
• There is sufficient evidence to conclude that the distribution of blood type for millionaires is the same as it is for Americans in general.
• There is sufficient evidence to conclude that the distribution of blood type for millionaires is not the same as it is for Americans in general.
• There is insufficient evidence to conclude that blood type and income are dependent.
• There is sufficient evidence to conclude that blood type and income are dependent.
• There is insufficient evidence to conclude that the distribution of blood type for millionaires is not the same as it is for Americans in general.
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