Respuesta :
Answer:
a) By the Central Limit Theorem, 245
b) 6.64
c) By the Central Limit Theorem, 245
d) 3.55
e) False
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 245, \sigma = 21[/tex]
a.) for a sample of size 10, state the mean of the sample mean.
By the Central Limit Theorem, 245
b.) for a sample of size 10, state the standard deviation of the sample mean (the "standard error of the mean").
[tex]s = \frac{21}{\sqrt{10}} = 6.64[/tex]
c.) for a sample of size 35, state the mean of the sample mean.
By the Central Limit Theorem, 245
d.) for a sample of size 35, state the standard deviation of the sample mean (the "standard error of the mean").
[tex]s = \frac{21}{\sqrt{35}} = 3.55[/tex]
e.) true or false: as sample size increases, standard deviation of the sample mean (the "standard error of the mean") also increases.
The standard error of the mean is given by [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]. So, as n(sample size) increases, s(standard deviation of the sample mean) decreases. So this is false.
