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class 2 - May 22 > chapter 8 > Flashcards

chapter 8 Flashcards

1
Q

what is an interval estimate

A

often computed by addition and subtracting a value

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2
Q

what is z a/2

A

critical value

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3
Q

if you have a high critical value then your margin of error will be

A

high

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4
Q

What is the purpose of an interval estimate

A

provides info about how close the point estimate is to the value of the pop parameter

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5
Q

What is the purpose of an interval estimate

A

provides info about how close the point estimate is to the value of the pop parameter

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6
Q

HOw do you calculate the margin of error with Q known

A

z a/2 x SE

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7
Q

If you have a 95% confidence what is your critical value and z-score

A

critical value is 1-.95 = 0.05
z a/2 = 0.05/2 = 0.025
z= -1.96

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8
Q

How do you calculate the interval when you know Q

A

x bar +- za/2 x SE (q / square root of n)

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9
Q

What is the confidence coefficent for a 95% confidence level

A

1 -.95 = 0.05

a = 0.05

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10
Q

What are the most commonly used Confidence Levels

A
  1. 90%
  2. 95%
  3. 99%
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11
Q

What are the most commonly used Confidence levels and their corresponding critical values and z scores

A
  1. 90% cv = .10 z = 1.645
  2. 95% CV = .05 z = 1.96
  3. 99% CV = .01 z = 2.576
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12
Q

In order to have a higher degree of confidence, the margin of error

A

and width of the interval must be larger

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13
Q

If the population does NOT follow a normal distribution for confidence intervals

A
  • the confidence interval will be appromate
  • quality of the approx. depends on
  1. distribution of the pop
  2. sample size

most applications, sample size of 30 or more is adequate

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14
Q

IF the population is not normally distributed but it is roughly symmetrical what sample size can produce a good approx confidence interval

A

n = 15 can be expected to provide a good aprpox. confidence interval

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15
Q

What if you have smaller sample sizes than 15

A

should only be used if the analyst believes pop distribution is at least approx. normal

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16
Q

How do you calculate an interval estimate if you don’t know Q

A

use t-distribution and df (n-1)

17
Q

at what level of df does the t-distribution become the standard normal distribution

A

more than 100 degrees of freedom

18
Q

As the number of df gets higher, what happens

A

the difference b/w the t-distribution and the normal distribution (z-table) becomes smaller and smaller

  • it becomes less variable and more closely resembles the standard normal distribution
19
Q

what is the mean of the t-distribution

A

0

20
Q

what it the formula for the interval for x bar when Q is not known

A

x bar +- s / (square root of n)

21
Q

how do you calcualte the standard error when you don’t know Q`

A

s = square root of (sum (x-x bar) squared / n-1

22
Q

When the pop does NOT follow normal distriubiton, the confidence interval will

A

be aprox
- the quality of the approx depends on

  1. distribution of the pop
  2. sample size
23
Q

most applcations what sample size is sufficent when Q is not known what should the sample size be at least

A

n is greater than or equal to 30

24
Q

what if the distribution is highly skewed or has outliers what should the minimum sample size be

A

sample size of 50 or more

25
Q

what if the distribution is roughly symmetrical what sample size should work

A

15 or more

26
Q

WHen determining the sample size needed for a desired margin of error how can you compute the planning value of Q

A
  1. use the estimate of the pop sd computed from the data of previous studies as a Planning value of Q
  2. use a pilot study to select a preliminary sample. the sample SD form this can be used as the planning values for Q
  3. use judgement for the values of Q
    ex. we might begin by estimating the largest and smallest data values in the pop

largest - smallest -> gives us an estimate for the range of data.

range / 4 = often suggested for a rough approx of the SD and thus acceptable planning value of Q

27
Q

What is the formula for the interval estimate for a Pop Proportion

A

p hat +- z a/2 (p hat +- square root p(1-P)/n)

28
Q

In practice how do you determine the sample size for Proportion (different ways)

A
  1. use the sample proportion from a previous sample of the same or similar units
  2. use a pilot study to select a preliminary sample
    - the sample proportion from this can be used as the planning value of P*
  3. use judgement or best guess p*
  4. if none of the proceeding alternatives apply, use planning value of p* =.50
29
Q

explain p*=.50 (planning value)

A

the largest value of P(1-P) occurs when P* = .50

  • this provides the largest sample size
  • this plays it safe
  • if sample size turns out to be different than .50, margin of error will be smaller than anticipated
    • thus, .50 will be sufficient to obtain the Margin of Error
30
Q

what is the desired margin of error for pop proportion

A

.10 or less

31
Q

what is also a common margin of error for pop proprotion other than .10

A

.03 or .04 margin of error is common

32
Q

in interval estimation, when the sample size becomes larger, the interval estimate

A

becomes narrower

33
Q

The absolute value of the difference between the point estimate and the pop parameter it estimates is the

A

sampling error

34
Q

as the number of df for a t distribution increases, the difference bw the t distribution and the standard normal distribution becomes

A

becomes smaller

35
Q

In an interval estimation, the t distribution is used only when the

A

sample standard deviation is used to estimate the pop standard deviation

36
Q

The ability of an interval estimate to contain the vlaue of the pop parameter is described by the

A

confidence level

37
Q

in general, higher confidence levels provide

A

wider confidence intervals

38
Q

an interval estimate is a range of values used to estimate

A

a population parameter

39
Q

when the level of confidence decreases, the margin of error

A

becomes smaller

class 2 - May 22 (9 decks)

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