a Compute the power of this test if the true mean speed is l

a) Compute the power of this test if the true mean speed is low as 95 meters per second. Round your answer to four decimal places (e.g. 98.7654)

Supercavitation is a propulsion technology for undersea vehicles that can greatly increase their speed. It occurs above approximately 50 meters per second, when the press drops off sufficiently to allow the water to dissociate into water vapor forming a gas bubble behind the vehicle. When the gas bubble completely encloses the vehicle, supercavitation is said to occur. Eight (n = 8) tests were conducted on a scale model of an undersea vehicle in a towing basin with the average observed speed Alpha = 0.05 a) Compute the power of this test if the true mean speed is low as 95 meters per second. Round your answer to four decimal places (e.g. 98.7654) Sigma = 4 meters per second. Use X = 102.2 meters per second. Assume that speed is normally distributed with

Solution

It is a one tailed test

The Z value for alpha= 0.05 is -1.645

(since the vlaue of mean lies to the left of 102.2)

.

Z = (x - X bar)/ (s/sqrt(n))

.

We got :

Z = -1.645

X bar = 102.2

s = 4

n = 8

.

On plugging these values we get

-1.645 = (x - 102.2) / (4/sqrt(8))

x = 99.8736

.

Now in prder to find the power for the mean = 95. we use the same formula with x bar = 95

Z = (99.8736 - 95) / (4/sqrt(8))

Z = 3.45

The P value for thsi value of Z is called the Power

P value can be obtained from the Z table

we get : P value = Power = 0.99972