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Answer:
a. A) Yes; as sample size increases, effect size increases.
b. A) The critical value increases.
Step-by-step explanation:
a.
If all possible samples of size N are drawn from a finite population, Np, without replacement, and the standard deviation of the mean values of the sampling distribution of means is determined then:
σx =d √N
d = σx . √N
d ∞ N
from this, we can say d is directly proportional to √N
where σx is the standard deviation of the sampling distribution of means and d is the standard deviation of the population’. The standard deviation of a sampling distribution of mean values is called the standard error of the means,
therefore, we can conclude that:
A) Yes; as sample size increases, effect size increases.
b.
In this estimate, tc is called the confidence coefficient for small samples, d is the standard deviation of the sample, x is the mean value of the sample and N is the number of members in the sample.
When determining the t-value, given by
t =(
(x−µ) /s) *
it is necessary to know the sample parameters x and s and the population parameter µ. x and s can be calculated for the sample, but usually an estimate has to be made of the population mean µ, based on the sample mean value.
from the above equation it can be deduced that t value is determined with the sample size, and as the sample size increases
A) The critical value increases.