S5. Confidence Intervals Flashcards

1
Q

What is the general form for confidence intervals?

A

(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.

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2
Q

Steps constructing a confidence interval for standardised mean with 95%

A
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3
Q

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

A

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

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4
Q

How does the confidence interval change with confidence level?

A

Increases with confidence level required.

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5
Q

How does the confidence interval change with the standard error?

A

Increases with the standard error of the statistic.

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6
Q

How does the confidence interval change with variance?

A

Increases with the variance of the data.

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7
Q

How does the confidence interval change with sample size?

A

Decreases as the sample size increases.

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8
Q

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

A

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

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9
Q

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

A

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

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10
Q

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

A

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

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11
Q

Confidence interval for a single mean

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

A
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12
Q

95% confidence interval for a single mean?

A
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13
Q

Confidence interval for the difference in two indpendent means

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

A
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14
Q

95% confidence interval for the difference in two independent means

A
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15
Q

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?

A
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16
Q

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

A
17
Q

Confidence interval for a single proportion

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

A
18
Q

95% confidence interval for a single proportion

A
19
Q

Confidence interval for the difference in two independent proportion

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

A
20
Q

95% confidence interval for the difference in two independent proportions

A
21
Q

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?

A
22
Q

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

A