Chapter 7: Confidence Intervals Flashcards

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1
Q

What is a confidence interval?

A

Specifies range of values to estimate location of unknown pop parameter

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2
Q

What does the margin of error accompany?

A

Confidence level

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3
Q

What does the confidence level tell us?

A

How likely our parameter is to lie within that interval

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4
Q

What does the confidence level and margin of error together tell us?

A

How accurate our estimate is likely to be

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5
Q

What is a point estimate?

A

Single statistic used as best estimate or a alike parameter

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6
Q

What does accuracy refer to?

A

Freedom from error

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7
Q

What is freedom from error?

A

Estimate differs from parameter of interests value

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8
Q

What is the interval estimate?

A

Range of values parameter is likely to fall

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9
Q

What is the essence of sampling theory?

A

Probability sample will yield results that closely resemble those if we measured whole pop

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10
Q

What is a probability sample?

A

Every element known prob of being selected

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11
Q

What does the law of large numbers tell us?

A

With large sample, sample statistics approximate pop parameters very closely

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12
Q

What does a confidence level specify?

A

Probability that our particular sample will contain pop parameter

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13
Q

What happens with higher confidence levels?

A

lower the risk that interval estimate doesn’t have parameter

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14
Q

What happens with a lower confidence level?

A

Increases risk interval estimate doesn’t have parameter

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15
Q

What happens in the case of the 99% confidence interval?

A

99% of all samples drawn from the same population with same measure at same time will be ± amount of sampling error

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16
Q

What would a correct interpretation look like?

A

95% confident that our interval estimate of 150 to 165 pounds will in fact contain the true population value.

17
Q

What do confidence interval statements actually mean?

A

we would expect to fail to capture the population mean in 5% of our samples (95)

18
Q

What does a confidence interval specify?

A

Range of values that we estimate an unknown population parameter will fall

19
Q

What does a confidence level specify?

A

Probability that population parameter will lie within that range

20
Q

What happens with interval width and level of confidence?

A

Higher confidence level, wider confidence interval will be

21
Q

What is the sampling error?

A

Whenever a sample rather than entire population is measured

22
Q

What is the margin of error?

A

Estimate amount of difference that we think is possible between our statistic and corresponding parameter

23
Q

What is the relationship between margin of error and sampling error?

A

How much sampling error we think is possible for given statistic

24
Q

What is confidence interval effected by?

A

Amount of variation in pop, sample size

25
Q

What happens with a greater sample size?

A

Smaller SD and smaller margin of error and sampling error

26
Q

What is the central limit theorem?

A

With repeated samples sampling distribution will eventually become normal

27
Q

What is a theoretical distribution?

A

Idea of conducting repeated samples infinitely

28
Q

What are the two assumptions you need to calculate a confidence interval?

A

Used random sampling, normal distribution

29
Q

What is the first scenario for calculating confidence interval?

A

Known pop sd

30
Q

What are the elements of the first scenario for calculating confidence interval?

A

Use z and normal distribution to get critical value, use o to get standard error

31
Q

What is the second scenario for calculating confidence interval?

A

Large sample and unknown pop sd

32
Q

What are the elements of the second scenario of calculating confidence interval?

A

Use z and normal distribution to get critical value, use s to estimate o for standard error

33
Q

What is the third scenario for calculating confidence interval?

A

Small sample and unknown pop sd

34
Q

What are the elements for the third scenario of calculating confidence interval?

A

Use t and t-distribution to determine critical value, use s to estimate o for standard error