A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMObelieves that certain types of doctors are more cost-effective than others. One theory is that Certification Levelis an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtainedindependent random samples of 19 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 19 physicians). In order to compare the mean charges for the threegroups, the data will be subjected to an analysis of variance.Write the null hypothesis tested by the ANOVA.
A) $\mathrm { H } _ { 0 } : \mu _ { \mathrm { C } } = \mu _ { \mathrm { E } } = \mu _ { \mathrm { I } }$
B) $\mathrm { H } _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$
C) $\mathrm { H } _ { 0 } : \mu _ { \mathrm { C } } = \mu _ { \mathrm { E } } = \mu _ { \mathrm { I } } = 0$
D) $\mathrm { H } _ { 0 } : \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 } = \mathrm { p } _ { 3 }$

Question

A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMObelieves that certain types of doctors are more cost-effective than others. One theory is that Certification Levelis an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtainedindependent random samples of 19 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 19 physicians). In order to compare the mean charges for the threegroups, the data will be subjected to an analysis of variance.Write the null hypothesis tested by the ANOVA. 
A) $\mathrm { H } _ { 0 } : \mu _ { \mathrm { C } } = \mu _ { \mathrm { E } } = \mu _ { \mathrm { I } }$
B) $\mathrm { H } _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$
C) $\mathrm { H } _ { 0 } : \mu _ { \mathrm { C } } = \mu _ { \mathrm { E } } = \mu _ { \mathrm { I } } = 0$
D) $\mathrm { H } _ { 0 } : \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 } = \mathrm { p } _ { 3 }$

Quizplus · Accepted Answer

The null hypothesis for an ANOVA test comparing the means of three groups (in this case, the mean charges for three groups of physicians with different certification levels) is that all group means are equal.

A Certain HMO Is Attempting to Show the Benefits of Managed