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Suppose two samples are taken. Sample 1 has a mean of 105 and a standard deviation of 15 and sample two has a mean of 100 and a standard deviation of 22. Assume the samples are taken on the same scale/variable.
Which of the following is a correct statement about these samples?

a. Sample 2 has more variability than sample 1.
b. Both samples are more or less the same.
c. Sample 1 has more variability than sample 2.
d. The mean of sample 2 is significantly higher than the mean of sample 1.

Respuesta :

christiankhoury

Answer:

a.

Step-by-step explanation:

Using the coefficient of variation, it is found that the correct option is:

a. Sample 2 has more variability than sample 1.

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The coefficient of variation for a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]cv = \frac{\sigma}{\mu}[/tex]

  • The higher the coefficient, the more variability is there in the distribution.

For Sample 1, [tex]\mu = 105, \sigma = 15[/tex], thus:

[tex]cv = \frac{15}{105} = 0.143[/tex]

For Sample 2, [tex]\mu = 100, \sigma = 22[/tex], thus:

[tex]cv = \frac{22}{100} = 0.22[/tex]

Due to the higher coefficient, Sample 2 has more variability, which means that option a is correct.

A similar problem is given at https://brainly.com/question/21304355

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