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2) Natural History magazine has published a listing of the maximum speeds, in mph, for a...

2) Natural History magazine has published a listing of the maximum speeds, in mph, for a wide variety of animals. A random sample of four of these animals, along with their maximum speeds, is shown below: Cheetah 70 mph Domestic Cat 30 mph Giraffe 32 mph Elephant 25 mph a) Compute the sample mean maximum speed of this sample of size 4. Show units. Do not approximate. b) The true mean maximum speed for all of the animals in this study is 30 mph. (  = 30 mph) Assuming there have been no mistakes in collecting, recording, or computing, find the sampling error. Show units.

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Expert Solution

Solution: a) Compute the sample mean maximum speed of this sample of size 4. Show units. Do not approximate.

Answer: The maximum speed of a random sample of 4 animals is given:

Now we have to find the sample mean of maximum speed of a sample of size 4. The sample mean is given below:

Where:

is the maximum speed of ith animal

n is the number of animals in the sample

Here in our case we have 4 animals. Therefore, the sample mean is:

  

  

mph

Hence, the sample mean of the maximum speed of a sample of size 4 is 39.25 mph

b) The true mean maximum speed for all of the animals in this study is 30 mph. (  = 30 mph) Assuming there have been no mistakes in collecting, recording, or computing, find the sampling error. Show units.

Answer: We are given the true mean of the maximum speed for all of the animals in this study is 30 mph. In other words, we are given:

mph

Now, we have to find the sampling error.

The sampling error is the difference between the value of a sample mean, , and the population mean, .

Therefore, the sampling error is:

mph

Hence, the sampling error is 9.25 mph

milcah answered 8 months ago
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