Sampling Distribution

Question 1

Sampling distribution of statistics - 3

Answer 1

• Focus on sampling distribution of a statistic instead of population
• Value of statistics obtained from population
• Distribution of all values of the statistic when all possible samples of same size n are taken from same population

Question 2

Sampling distribution of sample mean - 2

Answer 2

• Distribution of all possible sample means with all samples of size n taken from same population
• The sample mean of a population is approximately normal with
• • mean = miu
• • sd = sd/√n

Question 3

Behaviour of sample means - 2

Answer 3

• Sample means target the value of population mean.
• The mean of the sample mean is pop mean.
• The expected value of the sample mean is equal to pop mean.
• Distribution of sample means tends to be a normal distribution, as sample size increases.

Question 4

Sampling distribution of sample proportion - 2

Answer 4

• Distribution of sample proportions of all samples of size n taken from same population.
• For large n, sample proportion with population proportion p is approx normal
• • mean = p
• • sd = √p(1-p)/n

Question 5

Behaviour of sample proportions - 4

Answer 5

• Sample proportions target the value of the population proportions.
• The mean of the sample proportions is pop proportion.
• The expected value of the sample proportion is equal to pop proportion.
• The distribution of sample proportions approximates a normal distribution.

Question 6

Estimate of population proportion

Answer 6

• Sum of all elements which have a certain characteristic over the total number of the sample
• ^pn = (x1 + … + xn) / n