Information Regarding Random Samples of Annual Salaries in Thousands of Dollars)

question 117

Essay

Information regarding random samples of annual salaries in thousands of dollars) of doctors in three different specialties is shown below.
$$\begin{array} { l c c c } & \text { Pediatrics } & \text { Radiology } & \text { Pathology } \\\text { Sample size } & 12 & 10 & 11 \\\text { Average salary } & 120 & 186 & 240 \\\text { Sample variance } & 16 & 18 & 20\end{array}$$
a. Compute the overall mean .
b. State the null and alternative hypotheses to be tested.
c. Show the complete ANOVA table for this test including the test statistic.
d. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude?
e. Determine the p-value and use it for the test.

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Definitions:

Mollen Commission

An independent commission established to investigate corruption within a police department, particularly noted for its work with the New York City Police Department in the 1990s.

Sizeable Profits

Substantial financial gains that significantly exceed the usual or expected amount.

Wide Powers

Refers to the broad and extensive authority or influence that an entity or individual possesses.

Discretion

The freedom to decide what should be done in a particular situation, often implying judgment and prudence in making such decisions.