Module 6: Sampling Distributions
Indiana University administration reported that 56% of all faculty and staff members donated to the United Way campaign. A survey of a random sample of 100 faculty and staff members found that 60% have donated to United Way campaign. In this setting, which one is a parameter value and which one is a statistic value?
56% is a parameter value and 60% is a statistic value
Sampling Distribution
A probability distribution calculated from all possible random samples of a specific size taken from a population. It tells us how a statistic will be in repeated sampling
What sample sizes are considered sufficiently large for the sample distribution
A.)If both np>15 and nq>15 (for find confidence interval for proportion B.) If both npo>15 and nqo>15 (for test of hypothesis for proportion)
In general, which of the following statement is true about the sampling distribution of the sample mean? Formula: Standard error of sample mean {Standard deviation/sqrt{n}} rmula: Standard error of sample mean =LaTeX: \frac{\sigma}{\sqrt{n}} Increasing the sample size decreases the standard error. Increasing the sample size increases the standard error. Increasing the sample size does not change the standard error. Standard error will be negative by increasing the sample size.
Increasing the same size decreases the standard error
How large of a sample size is required to use CLT
Sample size of n>30
The natural tendency of randomly drawn samples to differ, from another is known as
Sampling variability or sampling error
Standard Error
Standard Deviation of a sampling Distribution of a statistic
Sampling distribution of sample mean
The distribution of all the same means that would arise from all possible random samples of the specific size from a population with a constraint
Sampling Distribution of a Sample Proportion
The distribution of all the sample proportions that would arise from all possible random samples of a specific size from a population with a constant probability of success
Sampling Error
The natural tendency of randomly drawn samples to differ from one another
Suppose studentsʹ ages follow a right skewed distribution with a mean of 25 years old and a standard deviation of 5 years. If we randomly sample 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect? Formula: standard error of sample mean= sigma/sqrt n
The standard error of the sample distribution is equal to 5 years
T/F In most situations, the true mean and true standard deviation of a population are unknown (unobserved) quantities that have to be estimated from sample data.
True
Central Limit Theorem
When n is sufficiently large, the shape of the sampling distribution of x bad will be approx. normal
Properties of the sampling distribution of sample mean
a.)The mean of the sampling distribution of x bar=the mean of the sampled population. b.)If a random sample of n observations is selected from a population with a normal distribution, the dsample distribution of x bar will be a normal distribution
The sampling distribution of a statistic is a probability distribution
calculated from all possible random samples of a specific size (n) taken from a population. all values the statistic can take in all possible samples of size n.
The Central Limit Theorem is considered powerful in statistics because
it works for any population distribution provided the sample size from a random sample is sufficiently large
In a large population of high school students who participated in the Indiana University High School Math Contest, the mean IQ is 120 with a standard deviation of 20. The distribution of IQ scores is normal. Suppose that 25 participants are chosen at random to be invited to a reception. The distribution of the sample mean IQ of the invitees is Formula: Standard error of sample mean = σ / sqrt:n
normal with mean 120, standard error 4.0
The central limit theorem says that when a random sample of size n is drawn from any population with mean (mu) μ and standard deviation (sigma) σ (read as sigma), then when n is sufficiently large (n ≥ 30)
the distribution of the sample mean is approximately normal.
Properties of the sample distribution of the sample proportion
when a large random sample is drawn from a population, the sampling distribution of p is modeled by a NORMAL model. Model is based on central limit theorem