Unit 3

Question 1

If the distribution of individual X’s is normal, what do we know about the distribution of the sample means?

Answer 1

• the distribution is also normal
• the mean is the same
• the standard deviation is sigma/sqrt(n)

Question 2

What is sampling distribution?

Answer 2

the distribution of values taken by the statistic in all possible samples of the same size from the same population

Question 3

Why is the standard deviation of x bar lower than that of X?

Answer 3

Averages are less variable than individual observations

Question 4

What does it mean for a statistic to be unbiased?

Answer 4

if the mean of its sampling distribution is equal to the true value of the parameter

Question 5

What does it mean for a statistic to be biased?

Answer 5

If it tends to systematically overestimate or underestimate the value of a parameter

Question 6

Is x bar biased or unbiased?

Answer 6

unbiased

Question 7

Is s^2 biased or unbiased?

Answer 7

unbiased

Question 8

What does asymptotically normally distributed mean?

Answer 8

The distribution is normal when the sample size is sufficiently large

Question 9

What is the central limit theorem?

Answer 9

Draw a SRS of size n from any population with mean mu and standard deviation sigma. When n is large, the sampling distribution of the sample mean is approximately normal

Question 10

How large must n be to apply the central limit theorem?

Answer 10

n >= 30

Question 11

What is a quantile plot?

Answer 11

• the y axis plots the data point
• the x axis plots what the z score should be in a normally distributed dataset for a datum in its percentile location

Question 12

Where is the median plotted in a quantile plot?

Answer 12

0

Question 13

What does the quantile plot of a normal distribution look like?

Answer 13

a straight line

Question 14

What is a simple random sample?

Answer 14

a sample of size n is a simple random sample of a population if all possible samples of size n are equally as likely to be the sample actually selected

Question 15

What are some possible explanations for why you might see an extreme sample?

Answer 15

• recording error
• it happened naturally; unlikely doesn’t mean impossible
• your perception was not the reality

Question 16

What does p-hat represent?

Answer 16

The sample proportion of successes in a SRS drawn from a large population with sample proportion p of successes

Question 17

What is he mean and standard deviation of p-hat?

Answer 17

mean: p
standard deviation: sqrt((p*(1-p))/n)

Question 18

When can you assume that the distribution of p-hat will be approximately normal?

Answer 18

• if n*p >= 10 and n(1-p) >= 10
• if the population is very large compared to the sample