Question

1.The Nearly Normal condition is met in one of either of two ways: the sample size is large or...

a.the population (and sample) distribution are already normal distribtuions.

b.we know the standard deviation of the population.

c.if the units we are measuring can only be positive (e.g. weights of chickens).

d.the two samples are independent.

2.Assume there exists a sample distribution that is normally distributed. For the sampling distribution to be approximately normal the central limit theorem requires the sample size to be...

a.The CLT is not needed here as the sampling distribution is already normal.

b.relatively small (around 50)

c.relatively large (more than 100)

d.It is impossible to tell

3.For an increase in sample size, we expect the sampling distribution of the sample mean to...

a.have a smaller standard error, that is the distribution gets more narrow.

b.have a larger standard error, that is the distribution gets more narrow.

c.have a larger standard error, that is the distribution gets more wide.

d.have a smaller standard error, that is the distribution gets more wide.

4.A sample has a sample size of 87.What is the degrees of freedom for associated with t* for this sampling distribution?

a.86

b.2.869

c.87

d.88

Answer 1

1. The two conditions are sample size is large or population is normal for which population standard deviation is known.

So answer for this is

b.we know the standard deviation of the population.

2. As the population is normal, sample mean is also normally distributed

So answer here is

a.The CLT is not needed here as the sampling distribution is already normal.

3. As n increases, standard deviation will decrease and distribution will become narrow as it will come closer to mean.

So answer here is

a.have a smaller standard error, that is the distribution gets more narrow.

4. df for t distribution is n-1

So for n=87, df is 87-1=86

So answer here is a.86