chapter 8

Question 1

what is an interval estimate

Answer 1

often computed by addition and subtracting a value

Question 2

what is z a/2

Answer 2

critical value

Question 3

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

Answer 3

high

Question 4

What is the purpose of an interval estimate

Answer 4

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

Question 5

What is the purpose of an interval estimate

Answer 5

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

Question 6

HOw do you calculate the margin of error with Q known

Answer 6

z a/2 x SE

Question 7

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

Answer 7

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

Question 8

How do you calculate the interval when you know Q

Answer 8

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

Question 9

What is the confidence coefficent for a 95% confidence level

Answer 9

1 -.95 = 0.05

a = 0.05

Question 10

What are the most commonly used Confidence Levels

Answer 10

1. 90%
2. 95%
3. 99%

Question 11

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

Answer 11

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

Question 12

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

Answer 12

and width of the interval must be larger

Question 13

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

Answer 13

• 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

Question 14

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

Answer 14

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

Question 15

What if you have smaller sample sizes than 15

Answer 15

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

Question 16

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

Answer 16

use t-distribution and df (n-1)

Question 17

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

Answer 17

more than 100 degrees of freedom

Question 18

As the number of df gets higher, what happens

Answer 18

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

Question 19

what is the mean of the t-distribution

Answer 19

0

Question 20

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

Answer 20

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

Question 21

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

Answer 21

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

Question 22

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

Answer 22

be aprox
- the quality of the approx depends on

1. distribution of the pop
2. sample size

Question 23

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

Answer 23

n is greater than or equal to 30

Question 24

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

Answer 24

sample size of 50 or more

Question 25

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

Answer 25

15 or more

Question 26

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

Answer 26

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

Question 27

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

Answer 27

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

Question 28

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

Answer 28

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

Question 29

explain p*=.50 (planning value)

Answer 29

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

Question 30

what is the desired margin of error for pop proportion

Answer 30

.10 or less

Question 31

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

Answer 31

.03 or .04 margin of error is common

Question 32

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

Answer 32

becomes narrower

Question 33

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

Answer 33

sampling error

Question 34

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

Answer 34

becomes smaller

Question 35

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

Answer 35

sample standard deviation is used to estimate the pop standard deviation

Question 36

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

Answer 36

confidence level

Question 37

in general, higher confidence levels provide

Answer 37

wider confidence intervals

Question 38

an interval estimate is a range of values used to estimate

Answer 38

a population parameter

Question 39

when the level of confidence decreases, the margin of error

Answer 39

becomes smaller