Question

Which of the following statements is correct?

a. sigma subscript x with bar on top end subscript equals fraction numerator sigma over denominator square root of n end fraction, where sigma = (sampled) population standard deviation and n = sample size--assuming n/N less or equal than .05, where N = (sampled) population size.

b. The sampling distribution of x with bar on top is either normally distributed, when the sampled population distribution is normal, or can be approximated by a normal distribution as the sample size becomes large, when the sampled population distribution is not normal.

c. By increasing the sample size, we increase the probability of obtaining a sample mean that is closer to the (sampled) population mean.

d. All of the above.

Answer 1

Solution:

All of the above are CORRECT

a)   =  

where   =  (sampled)population standard deviation and n = sample size assuming n/N   0.05, where N = (sampled) population size.

This is correct . is standard deviation of sampling distribution of sample mean . It is also called as standard error of the mean.

b)The sampling distribution of is either normally distributed, when the sampled population distribution is normal, or can be approximated by a normal distribution as the sample size becomes large, when the sampled population distribution is not normal.

This is correct.

c) By increasing the sample size, we increase the probability of obtaining a sample mean that is closer to the (sampled) population mean.

Correct.

As sample size increases , error decreases and sample mean goes closer to population mean.

So , all of the above. are correct