A common estimate of the top speed of a cheetah is 60mph, although cheetahs ofte

Question

A common estimate of the top speed of a cheetah is 60mph, although cheetahs often exceed this speed, and have even been documented running at 72mph. Researchers wanted to know if the how accurate the common estimate of 60mph was. They measured the top speed of 35 cheetahs in the wild and found the average speed of cheetahs in their sample was 59.526 mph. Other research indicated that the standard deviation (sigma) of speeds is 3.2mph. H_0: mu = 60: H_A: mu 60. Explain what each of the following would mean in terms specific to the problem. a. A Type 1 error b. A Type 2 error c. A Correct Decision d. If the result of a hypothesis test lead to the conclusion that the null hypothesis should not be rejected, but the true mean was 60mph, what kind of error was made, or was the correct decision made? Explain your reasoning.

Explanation / Answer

Answer:

a).

Type I error—rejecting the null hypothesis when it is true.

We reject the null hypothesis of true mean is 60mph when actually true mean was 60 mph.

b).

Type II error : If the alternative hypothesis is actually true, but we fail to reject the null hypothesis.

We fail reject the null hypothesis of true mean is 60mph when actually true mean was different from 60 mph.

C:

Correct decision:

We fail to reject the null hypothesis of true mean is 60mph when actually true mean was 60 mph.

OR

We reject the null hypothesis of true mean is 60mph when actually true mean was different from 60 mph.

d).

Correct decision was made. We fail to reject the null hypothesis of true mean is 60mph when actually true mean was 60 mph.

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