Respuesta :
Answer:
a. Mean = 100, S.D. = 3.333
b. Mean = 100, S.D. = 2.582
c. Mean = 100, S.D. = 1.667
d. Mean = 100, S.D. = 1.414
e. Mean = 100, S.D. = 1
f. Mean = 100, S.D. = 0.5
Step-by-step explanation:
The question is incomplete:
Population mean: 100
Population standard deviation: 10.
The mean for any sampling distribution is equal to the population mean.
The standard deviation for the sampling distribution depends on the population standard deviation and the sample size as:
[tex]\sigma_s=\dfrac{\sigma}{\sqrt{n}}[/tex]
We can calculate the parameters of the sampling distributions as:
a. n = 9
[tex]\mu_s=\mu=100\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{9}}=\dfrac{10}{3}=3.333[/tex]
b. n = 15
[tex]\mu_s=\mu=100\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{15}}=\dfrac{10}{3.873}=2.582[/tex]
c. n = 36
[tex]\mu_s=\mu=100\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{36}}=\dfrac{10}{6}=1.667[/tex]
d. n = 50
[tex]\mu_s=\mu=100\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{50}}=\dfrac{10}{7.071}=1.414[/tex]
e. n = 100
[tex]\mu_s=\mu=100\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{100}}=\dfrac{10}{10}=1[/tex]
f. n = 400
[tex]\mu_s=\mu=100\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{400}}=\dfrac{10}{20}=0.5[/tex]
