Conditions for Sampling Distribution

According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated. A school district has 180 incoming kindergarten children.

Which of the following is true concerning the shape of the sampling distribution?

• The sampling distribution is normal because n > 30

• The sampling distribution is not normal because nq is < 30

• The sampling distribution is normal because 93% of 180 is > 10

• The sampling distribution is normal because np and nq are both > 10

A distribution showing the sample means of all sample of size n of a population is called

• Normal Distribution

• Binomial Distribution

• Sampling Distribution

• Uniform Distribution

The Central Limit Theorem can be applied to find the distribution of the sample mean under certain conditons. These conditions are:

• The sample is limited to data within one standard deviation of the centre.

• The sample mean is positive.

• The sample size is large, and the population from which the random sample is drawn has finite variance.

• The random variable representing the population is restricted to counting data.

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25. 
What is the standard error of the sampling distribution?

• 200

• 16

• 25

• 4

Answer explanation

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25. 
What is the standard error of the sampling distribution?

• 200

• 16

• 25

• 4

Given a population with proportion p=.35. Which of the following is true of a sample of size 50? Assume the sample is taken randomly and all individuals are independent of each other, and we have not violated the 10% rule.

• Pre-conditions for normality have not been met (the sample is too small).

• Sample is big enough, p= .50 and sampling distribution = .35

• Sample is big enough, p= .35 and sampliing distribution = .067

• Sample is big enough, p= .35 and the sampling distribution = .107

Assume we have met all the pre-conditions to ensure our distribution of all possible sample proportions is normal. If I'm drawing a sample of size 100 (n=100) from a population that is 49% men (so p=.49), what is the probability that my sample proportion p-hat will be less than .40? Remember this proportion is normally distributed. 

P(p-hat<.40)=...

• .036

• .452

• .490

• .964

Assume we are sampling to find the percent of people of Asian descent from a population that is actually 20% Asian (p=.2). Which of the following sample sizes would meet the minimum requirement for assuming the distribution of sampling proportions is normal? (Hint-remember your pre-conditions). Select ALL that would be considered big enough.

• 10

• 20

• 50

• 75

Which conditions hold true based on the central limit theorem? (Check all that apply.)

• If samples of size n = 30 are drawn from a population, then the sampling distribution of sample means approximate a normal distribution

• If samples of size n < 30 are drawn from a population, then the sampling distribution of sample means approximate a normal distribution

• If samples of size n > 30 are drawn from a population, then the sampling distribution of sample means approximate a normal distribution

• If samples of size n < 30 are drawn from a population which is normally distributed, then the sampling distribution of sample means is also normally distributed

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population

• The Sample

• The Sampling Distribution