A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 27 physicians from each of the three certification levels-Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-and recorded the total per-member, per-month charges for each (a total of 27 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Write the null hypothesis tested by the ANOVA.
A) $H _ { 0 } : \mu _ { \mathrm { C } } = \mu _ { \mathrm { E } } = \mu \mathrm { I }$
B) $H _ { 0 } : \mu _ { \mathrm { C } } = \mu _ { \mathrm { E } } = \mu _ { \mathrm { I } } = 0$
C) $H _ { 0 } : p _ { 1 } = p _ { 2 } = p _ { 3 }$
D) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$

Question

A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 27 physicians from each of the three certification levels-Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-and recorded the total per-member, per-month charges for each (a total of 27 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Write the null hypothesis tested by the ANOVA. 
A) $H _ { 0 } : \mu _ { \mathrm { C } } = \mu _ { \mathrm { E } } = \mu \mathrm { I }$
B) $H _ { 0 } : \mu _ { \mathrm { C } } = \mu _ { \mathrm { E } } = \mu _ { \mathrm { I } } = 0$
C) $H _ { 0 } : p _ { 1 } = p _ { 2 } = p _ { 3 }$
D) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$

Quizplus · Accepted Answer

The null hypothesis tested by the ANOVA is that the mean charges for the three groups are equal. This is represented by the hypothesis $H _ { 0 } : \mu _ { \mathrm { C } } = \mu _ { \mathrm { E } } = \mu \mathrm { I }$.

A Certain HMO Is Attempting to Show the Benefits of Managed