Module 6

Question 1

IMPORTANT NOTES
Statistics class becomes increasingly tough
No other choice but to study hard
Don’t give up and hang in there
It’s not as complicated as it appears
Examples will be shown

Answer 1

分かります

Question 2

A random sample of 50 individuals resulted in a mean income of $15,000. The population standard deviation is known to be $1,000. What is the 95% confidence interval for the true mean income of the population?

Answer 2

Sample size (n): 50
Sample mean (x̄): 15000
Population standard deviation (σ): 1000
95% confidence interval: Z(↓) 0.025 = -1.96

Question 3

as the sample size gets large enough…

the sampling distribution of the sample mean (x̄) becomes almost normal regardless of shape of population.

Answer 3

Central Limit Theorem

Question 4

Sample Mean Sampling Distribution: If the population is not Normal or not known

Answer 4

We can apply the Central Limit Theorem:
-Even if the population is not normal or not known,
-…sample means from the population will be approx. normal as long as the sample size is large enough

Question 5

A ________ ____________ is a distribution of all the possible values of a sample statistic for a given sample size selected from a population.

Answer 5

Sampling Distribution

Question 6

For example, you sample 50 students from your college regarding their mean GPA, if you obtained many different samples of size 50, you will compute a different mean for each sample. We are interested in the distribution of all potential mean GPAs we might calculate for samples of 50 students.

Answer 6

Sampling Distributions

Question 7

Sample mean ________ ____________: Standard Error of the mean

-Different samples of the same size from the same population will yield different sample means.
-A measure of the variability in the mean from sample to sample is given by the Standard Error of the Mean.

Answer 7

Sampling Distribution

Question 8

(Cont.) -A measure of the variability in the mean from sample to sample is given by the Standard Error of the Mean.
(This assumes that sampling is with replacement or sampling is without replacement from an infinite population.)
-Note that the standard error of the mean decreases as the sample size increases.

Answer 8

SE = σ / √n

Question 9

(Module 6.2)
If a population is normal with mean μ and standard deviation σ of x̄ is also normally distributed with mean µ and standard deviation

Answer 9

Sample mean Sampling Distribution: If the Population is Normal