In Testing the Hypotheses $H _ { 0 } : \mu = 20$

question 31

Essay

In testing the hypotheses $H _ { 0 } : \mu = 20$ . $H _ { 1 } : \mu < 20$ .
the following information was given: $\sigma = 8.1 , \quad n = 100 , \quad \bar { x } = 18.1 , \quad \alpha = 0.025$ .
a. Calculate the value of the test statistic.
b. Set up the rejection region.
c. Determine the p-value.
d. Interpret the result.

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Definitions:

Compound Motor

A type of DC motor that combines both series and shunt winding to offer high starting torque and good speed regulation.

Series and Shunt

Terms used to describe configurations in electrical circuits; "series" refers to components connected end-to-end, while "shunt" refers to components connected parallel to each other.

Constant Speed Motor

A motor that maintains a uniform speed under varying loads, often achieved through feedback mechanisms or specialized designs.

DC Motor

A type of electric motor that runs on direct current electricity, used in a wide variety of applications from vehicles to industrial machinery.