S5. Confidence Intervals

Question 1

What is the general form for confidence intervals?

Answer 1

(sample statistic ± a number of s.d. × standard error)

Width of the confidence interval depends on the number of standard errors either side of zero you need to go to cover a fixed probability.

Question 2

Steps constructing a confidence interval for standardised mean with 95%

Answer 2

Question 3

Typical values for 90%, 95% and 99% confidence intervals

Answer 3

90: ±1.645 standard errors
95: ±1.96 standard errors
99: ±2.58 standard errors

Question 4

How does the confidence interval change with confidence level?

Answer 4

Increases with confidence level required.

Question 5

How does the confidence interval change with the standard error?

Answer 5

Increases with the standard error of the statistic.

Question 6

How does the confidence interval change with variance?

Answer 6

Increases with the variance of the data.

Question 7

How does the confidence interval change with sample size?

Answer 7

Decreases as the sample size increases.

Question 8

If we have a 95% confidence level, what does this tell us?

Answer 8

That in approx. 95% of them, the population parameter lies in their range. Each has a 95% change of covering it.

Question 9

Right or wrong? “Interpreting confidence intervals in terms of the probabilistic behaviour of the population parameter is wrong.”

Answer 9

Wrong: there is a 95% change that the population parameter lies in the interval [a, b].

Question 10

Right or wrong? “Interpreting confidence intervals in terms of the probabilistic behaviour of the interval is right”

Answer 10

Right: there is a 95% probability that the interval [a,b] will contain the population parameter.

Question 11

Confidence interval for a single mean

What is the population parameter and esitmator for standard error of the sampling distribution?

Answer 11

Question 12

95% confidence interval for a single mean?

Answer 12

Question 13

Confidence interval for the difference in two indpendent means

What is the population parameter and esitmator for standard error of the sampling distribution?

Answer 13

Question 14

95% confidence interval for the difference in two independent means

Answer 14

Question 15

Confidence interval for the difference in two dependent mean (paired data)

What is the population parameter and esitmator for standard error of the sampling distribution?

Answer 15

Question 16

95% confidence interval for the difference in two dependent mean (paired data)

Answer 16

Question 17

Confidence interval for a single proportion

What is the population parameter and esitmator for standard error of the sampling distribution?

Answer 17

Question 18

95% confidence interval for a single proportion

Answer 18

Question 19

Confidence interval for the difference in two independent proportion

What is the population parameter and esitmator for standard error of the sampling distribution?

Answer 19

Question 20

95% confidence interval for the difference in two independent proportions

Answer 20

Question 21

Confidence interval for the difference in two dependent proprtions (paired data)

What is the population parameter and esitmator for standard error of the sampling distribution?

Answer 21

Question 22

95% confidence interval for the difference in two dependent proprtions (paired data)

Answer 22