Unit 4

Question 1

Why isn’t it good to report a statistic that you have 100% confidence in?

Answer 1

It will usually be meaningless. We need to make sure we can make an interval where we are confident it overlaps the parameter while not making it overly wide

Question 2

What is statistical inference?

Answer 2

Using sample data to make inferences about the population

Question 3

Why do we use confidence intervals instead of points?

Answer 3

Mathematically, the parameter and statistic will never be exactly equal

Question 4

What does confidence mean in statistics?

Answer 4

If I use the same method to make my interval, a target % of the time it will contain the parameter (a statement on how often our method is going to work)

Question 5

What is the form of confidence intervals?

Answer 5

estimate +- sampling error

Question 6

What is an estimate?

Answer 6

our best guess at the true value

Question 7

What is the sampling error?

Answer 7

(margin of error): how much inaccuracy we could generally expect due to sampling variability

Question 8

What is a general interpretation of a confidence interval?

Answer 8

If we repeatedly took samples of the same size from the same population and constructed confidence intervals in a similar manner then C% of all such intervals would contain the true mean mu (where C is the level of confidence

Question 9

What happens if we multiply the sampling error by 1/k?

Answer 9

The sample size is multiplied by k^2

Question 10

What does T represent?

Answer 10

the number of standard deviations x bar is from mu with n - 1 degrees of freedom (for every additional thing we’re estimating, we lose some precision)

Question 11

What is the standard error?

Answer 11

s/sqrt(n): it estimates the standard deviation of xbar
or
sqrt(p(1-p-hat)/n): it estimates the standard deviation of p

Question 12

Where do you use the t-statistic instead of z?

Answer 12

Where sigma is unknown. We will use s in place of sigma which means we need ta/2 values instead of Za/2 values

Question 13

What does changing the sample size do to a t distribution?

Answer 13

A larger sample size will make it narrower (centre stays the same)

Question 14

What are degrees of freedom?

Answer 14

For each element in our sample, we can do one more thing with our analysis. The t-distribution requires us to estimate sigma by s so we “use up” one degree of freedom leaving us with n - 1

Question 15

What are some differences between the t-distribution and z-distribution?

Answer 15

• the t-distribution is smaller near the center
• the t-distribution has wider tails
• as n increases it moves closer to the z-distribution

Question 16

Can we find confidence intervals for distributions that are not normally distributed?

Answer 16

Yes, but only with large sample sizes and they will be approximate

Question 17

What is p-star?

Answer 17

Either an educated guess at the true value (maybe from historical data) or, 0.5