M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn...

33
M32 Margin of Error Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn how to calculate the m.o.e. for two situations: when the true population std. dev., , is known and when its unknown. Learn how to use the

Transcript of M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn...

Page 1: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002

Lesson Objectives

Learn the meaning of “margin of error,” or “m.o.e.”

Learn how to calculate them.o.e. for two situations: when the true population std. dev., ,is known and when its unknown.

Learn how to use the m.o.e. toconstruct a confidence interval.

Page 2: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 2 Department of ISM, University of Alabama, 1995-2002

“Margin of Error” for estimating

the True Mean of a population.

“Margin of Error” for estimating

the True Mean of a population.

m.o.e. at 95% confidence =“The amount that when added and subtracted to the true population meanwill define a region that will includethe middle 95% of all possible X-bar values.”

Page 3: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 3 Department of ISM, University of Alabama, 1995-2002

= true population mean.

Find the interval around the mean where 95% of all possible sample means will lie.

X

.95

? ? -1.96 0 +1.96 Z

.025.025

Illustration of “Margin of Error”

Page 4: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 4 Department of ISM, University of Alabama, 1995-2002

? - Z = n

+1.96 =? - n

? = + 1.96 n

Margin of ErrorMargin of Error

Page 5: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 5 Department of ISM, University of Alabama, 1995-2002

1.96 n x

standard error of the mean

Margin of Error for 95% confidence:

m.o.e. =

Page 6: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 6 Department of ISM, University of Alabama, 1995-2002

General form for “margin of error”when is known:

m.o.e. = Z n

2

Z 2

appropriate percentile from the standard normal distribution,i.e., the Z table.

where is the

Page 7: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 7 Department of ISM, University of Alabama, 1995-2002

Explanation of symbol:

Z ~ N(0,1)

/ 2

0 Z / 2

Z / 2 cuts off the top tail at area = /2

.5- /2

Page 8: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 8 Department of ISM, University of Alabama, 1995-2002

Amount ofconfidence

Area ineach tail

Table value

.95

.90

.80

.98

.0250

.0500

.1000

.0100

1.96

1.645

1.28

2.33

1 - / 2 Z / 2

Examples

Page 9: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 9 Department of ISM, University of Alabama, 1995-2002

(1-)100% Confidence Interval:

Point estimate m.o.e.

(1-)100% is the amount of confidence desired.

.95 confidence = .05 risk

Page 10: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 10 Department of ISM, University of Alabama, 1995-2002

m.o.e. = Z n

2

= 2.33 10 4 = 5.825 gal.

= Z.01 10

16

Estimate with 98% confidence the mean gallons of water used per shower for Dallas Cowboys after a game if the true standard deviation is known to be 10 gallons. The sample mean for 16 showers is 30.00 gal.

Example 1

Page 11: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 11 Department of ISM, University of Alabama, 1995-2002

30.00 5.825

Point estimate m.o.e.

or24.175 to 35.825 gallons

Example 1, continued . . .

98% confidence interval:

Page 12: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 12 Department of ISM, University of Alabama, 1995-2002

I am 98% confident that the true mean gallons

of water used per shower for Dallas Cowboys after a game will fall within the interval 24.175 to 35.825 gallons.

Example 1, Statement in the L.O.P.

A statement in A statement in L.O.P.L.O.P. must contain four parts: must contain four parts: 1. amount of 1. amount of confidenceconfidence.. 2. the 2. the parameterparameter being estimated in L.O.P. being estimated in L.O.P. 3. the 3. the populationpopulation to which we generalize to which we generalize in L.O.P. in L.O.P. 4. the 4. the calculated intervalcalculated interval. .

Page 13: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 13 Department of ISM, University of Alabama, 1995-2002

• Replace with s.

• replace z with t.

What do we do if the true population standard deviation is unknown?

Page 14: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 14 Department of ISM, University of Alabama, 1995-2002

General form for “margin of error”when is UN-known:

m.o.e. = t sn

2,n–1

sx

“estimated” standard error of the mean

t 2

,n–1where is the

appropriate percentile from the t-distribution.

Page 15: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 15 Department of ISM, University of Alabama, 1995-2002

Explanation of symbol:

t-distribution

/ 2

0 t / 2 , n–1

t / 2, n-1 cuts off the top tail at area = /2

Use the t-table to find the value.

Page 16: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

0 t

Table gives right-tail area.(e.g., for a right-tail areaof 0.025 and d.f. = 15,the t value is 2.131.)

0.1 0.05 0.025 0.01 0.005

d.f. = 1 3.078 6.314 12.706 31.821 63.6562 1.886 2.920 4.303 6.965 9.9253 1.638 2.353 3.182 4.541 5.8414 1.533 2.132 2.776 3.747 4.6045 1.476 2.015 2.571 3.365 4.0326 1.440 1.943 2.447 3.143 3.7077 1.415 1.895 2.365 2.998 3.4998 1.397 1.860 2.306 2.896 3.3559 1.383 1.833 2.262 2.821 3.250

10 1.372 1.812 2.228 2.764 3.16911 1.363 1.796 2.201 2.718 3.10612 1.356 1.782 2.179 2.681 3.05513 1.350 1.771 2.160 2.650 3.01214 1.345 1.761 2.145 2.624 2.97715 1.341 1.753 2.131 2.602 2.94716 1.337 1.746 2.120 2.583 2.92117 1.333 1.740 2.110 2.567 2.89818 1.330 1.734 2.101 2.552 2.87819 1.328 1.729 2.093 2.539 2.86120 1.325 1.725 2.086 2.528 2.84521 1.323 1.721 2.080 2.518 2.83122 1.321 1.717 2.074 2.508 2.81923 1.319 1.714 2.069 2.500 2.80724 1.318 1.711 2.064 2.492 2.79725 1.316 1.708 2.060 2.485 2.78726 1.315 1.706 2.056 2.479 2.77927 1.314 1.703 2.052 2.473 2.77128 1.313 1.701 2.048 2.467 2.76329 1.311 1.699 2.045 2.462 2.75630 1.310 1.697 2.042 2.457 2.75031 1.309 1.696 2.040 2.453 2.74432 1.309 1.694 2.037 2.449 2.73833 1.308 1.692 2.035 2.445 2.73334 1.307 1.691 2.032 2.441 2.72835 1.306 1.690 2.030 2.438 2.724

0.1 0.05 0.025 0.01 0.005

36 1.306 1.688 2.028 2.434 2.71937 1.305 1.687 2.026 2.431 2.71538 1.304 1.686 2.024 2.429 2.71239 1.304 1.685 2.023 2.426 2.70840 1.303 1.684 2.021 2.423 2.70441 1.303 1.683 2.020 2.421 2.70142 1.302 1.682 2.018 2.418 2.69843 1.302 1.681 2.017 2.416 2.69544 1.301 1.680 2.015 2.414 2.69245 1.301 1.679 2.014 2.412 2.690

97 1.290 1.661 1.985 2.365 2.62798 1.290 1.661 1.984 2.365 2.62799 1.290 1.660 1.984 2.365 2.626

100 1.290 1.660 1.984 2.364 2.6261.282 1.645 1.960 2.326 2.576

Want 95% CI,n = 20,

/2 = .025d.f. = 19

t.025, 19= 2.0932.093

Page 17: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

0 t

0.1 0.05 0.025 0.01 0.005

d.f. = 1 3.078 6.314 12.706 31.821 63.6562 1.886 2.920 4.303 6.965 9.9253 1.638 2.353 3.182 4.541 5.8414 1.533 2.132 2.776 3.747 4.6045 1.476 2.015 2.571 3.365 4.0326 1.440 1.943 2.447 3.143 3.7077 1.415 1.895 2.365 2.998 3.4998 1.397 1.860 2.306 2.896 3.3559 1.383 1.833 2.262 2.821 3.250

10 1.372 1.812 2.228 2.764 3.16911 1.363 1.796 2.201 2.718 3.10612 1.356 1.782 2.179 2.681 3.05513 1.350 1.771 2.160 2.650 3.01214 1.345 1.761 2.145 2.624 2.97715 1.341 1.753 2.131 2.602 2.94716 1.337 1.746 2.120 2.583 2.92117 1.333 1.740 2.110 2.567 2.89818 1.330 1.734 2.101 2.552 2.87819 1.328 1.729 2.093 2.539 2.86120 1.325 1.725 2.086 2.528 2.84521 1.323 1.721 2.080 2.518 2.83122 1.321 1.717 2.074 2.508 2.81923 1.319 1.714 2.069 2.500 2.80724 1.318 1.711 2.064 2.492 2.79725 1.316 1.708 2.060 2.485 2.78726 1.315 1.706 2.056 2.479 2.77927 1.314 1.703 2.052 2.473 2.77128 1.313 1.701 2.048 2.467 2.76329 1.311 1.699 2.045 2.462 2.75630 1.310 1.697 2.042 2.457 2.75031 1.309 1.696 2.040 2.453 2.74432 1.309 1.694 2.037 2.449 2.73833 1.308 1.692 2.035 2.445 2.73334 1.307 1.691 2.032 2.441 2.72835 1.306 1.690 2.030 2.438 2.724

0.1 0.05 0.025 0.01 0.005

36 1.306 1.688 2.028 2.434 2.71937 1.305 1.687 2.026 2.431 2.71538 1.304 1.686 2.024 2.429 2.71239 1.304 1.685 2.023 2.426 2.70840 1.303 1.684 2.021 2.423 2.70441 1.303 1.683 2.020 2.421 2.70142 1.302 1.682 2.018 2.418 2.69843 1.302 1.681 2.017 2.416 2.69544 1.301 1.680 2.015 2.414 2.69245 1.301 1.679 2.014 2.412 2.690

97 1.290 1.661 1.985 2.365 2.62798 1.290 1.661 1.984 2.365 2.62799 1.290 1.660 1.984 2.365 2.626

100 1.290 1.660 1.984 2.364 2.6261.282 1.645 1.960 2.326 2.576

Want 98% CI,n = 33,

/2 = .01d.f. = 32

t.01, 32= 2.4492.449

Table gives right-tail area.(e.g., for a right-tail areaof 0.025 and d.f. = 15,the t value is 2.131.)

Page 18: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

0 t

0.1 0.05 0.025 0.01 0.005

d.f. = 1 3.078 6.314 12.706 31.821 63.6562 1.886 2.920 4.303 6.965 9.9253 1.638 2.353 3.182 4.541 5.8414 1.533 2.132 2.776 3.747 4.6045 1.476 2.015 2.571 3.365 4.0326 1.440 1.943 2.447 3.143 3.7077 1.415 1.895 2.365 2.998 3.4998 1.397 1.860 2.306 2.896 3.3559 1.383 1.833 2.262 2.821 3.250

10 1.372 1.812 2.228 2.764 3.16911 1.363 1.796 2.201 2.718 3.10612 1.356 1.782 2.179 2.681 3.05513 1.350 1.771 2.160 2.650 3.01214 1.345 1.761 2.145 2.624 2.97715 1.341 1.753 2.131 2.602 2.94716 1.337 1.746 2.120 2.583 2.92117 1.333 1.740 2.110 2.567 2.89818 1.330 1.734 2.101 2.552 2.87819 1.328 1.729 2.093 2.539 2.86120 1.325 1.725 2.086 2.528 2.84521 1.323 1.721 2.080 2.518 2.83122 1.321 1.717 2.074 2.508 2.81923 1.319 1.714 2.069 2.500 2.80724 1.318 1.711 2.064 2.492 2.79725 1.316 1.708 2.060 2.485 2.78726 1.315 1.706 2.056 2.479 2.77927 1.314 1.703 2.052 2.473 2.77128 1.313 1.701 2.048 2.467 2.76329 1.311 1.699 2.045 2.462 2.75630 1.310 1.697 2.042 2.457 2.75031 1.309 1.696 2.040 2.453 2.74432 1.309 1.694 2.037 2.449 2.73833 1.308 1.692 2.035 2.445 2.73334 1.307 1.691 2.032 2.441 2.72835 1.306 1.690 2.030 2.438 2.724

0.1 0.05 0.025 0.01 0.005

36 1.306 1.688 2.028 2.434 2.71937 1.305 1.687 2.026 2.431 2.71538 1.304 1.686 2.024 2.429 2.71239 1.304 1.685 2.023 2.426 2.70840 1.303 1.684 2.021 2.423 2.70441 1.303 1.683 2.020 2.421 2.70142 1.302 1.682 2.018 2.418 2.69843 1.302 1.681 2.017 2.416 2.69544 1.301 1.680 2.015 2.414 2.69245 1.301 1.679 2.014 2.412 2.690

97 1.290 1.661 1.985 2.365 2.62798 1.290 1.661 1.984 2.365 2.62799 1.290 1.660 1.984 2.365 2.626

100 1.290 1.660 1.984 2.364 2.6261.282 1.645 1.960 2.326 2.576

Want 90% CI,n = 600,

/2 = .05d.f. = 599

t.05, = 1.6451.645Same as Normal

Table gives right-tail area.(e.g., for a right-tail areaof 0.025 and d.f. = 15,the t value is 2.131.)

Page 19: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 19 Department of ISM, University of Alabama, 1995-2002

t-dist.Z

Bell shaped, symmetric

Mean

Std. dev.

As “n–1” increases, “tn–1” approaches “Z”

Degrees of freedom

= 0

> 1

Yes Yes

= 0

= 1

“n-1”“”

Comparison of “Z” and “t”

Page 20: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 20 Department of ISM, University of Alabama, 1995-2002

= 2.602 10.4 4 = 6.765 gal.

= t.01, 15 10.4

16

Estimate with 98% confidence the mean gallons of water used per shower at the UA Student Rec Center. For a sample of 16 showers the mean was 30.00 gallons and the standard deviation was 10.4 gallons.

Example 2

m.o.e. sn

t 2

, n-1

Page 21: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 21 Department of ISM, University of Alabama, 1995-2002

30.00 6.765

Point estimate m.o.e.

or23.235 to 36.765 gallons

Example 2, continued . . .

98% confidence interval:

Page 22: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 22 Department of ISM, University of Alabama, 1995-2002

I am 98% confident that the true mean gallons

of water used per shower for at the UA Student Rec Center will fall within the interval 23.235 to 36.765 gallons.

Example 2, Statement in the L.O.P.

A statement in A statement in L.O.P.L.O.P. must contain four parts: must contain four parts: 1. amount of 1. amount of confidenceconfidence.. 2. the 2. the parameterparameter being estimated in L.O.P. being estimated in L.O.P. 3. the 3. the populationpopulation to which we generalize to which we generalize in L.O.P. in L.O.P. 4. the 4. the calculated intervalcalculated interval. .

Page 23: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 23 Department of ISM, University of Alabama, 1995-2002

To get a smaller Margin of Error:

Increase “n”.

Decrease the amount of confidence desired.

= 1.96 n

Margin of Error for 95% confidence:

Page 24: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 24 Department of ISM, University of Alabama, 1995-2002

Confidence vs. Probability

BEFORE a sample is collected, there is a 95% probability that the future to be computed sample mean, will fall within m.o.e. units of .

AFTER the sample is collected, the computed sample mean either fell within m.o.e. units of or it did not. After the event, it does not make sense to talk about probability.

Analogy: Suppose you own 95 tickets in a 100-ticket lottery. The drawing was held one hour ago, but you don’t know the result.

P(win) = 0 or 1, but you are very CONFIDENT that you have won the lottery.

Page 25: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 25 Department of ISM, University of Alabama, 1995-2002

What sample size is needed to estimate the mean mpg of Toyota Camrys with an m.o.e. of 0.2 mpg at 90%confidence if the pop. std. dev. is 0.88 mpg?

m.o.e. = Z n

2

0.2 = 1.645 0.88n

n =1.6452 0.882

0.22 = 52.39

Round

UP,use 53

Round

UP,use 53

Page 26: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 26 Department of ISM, University of Alabama, 1995-2002

Interpretations of theInterpretations of theConfidence Interval for Confidence Interval for

• If we took many, many samples of size n, and calculated a confidence interval for each, then I would expect that 95% of all these many intervals would contain the true mean, and 5% would not.

Page 27: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 27 Department of ISM, University of Alabama, 1995-2002

Example 3: A car rental agency wants to estimate the average mileage driven by its customers. A sample of 225 customer receipts, selected at random, yields an average of 325 miles. Assuming that the population standard deviation is 120 miles, construct a 95% confidence interval for the population average mileage.

325 1.96 * 120 / 15325 15.680

309.32, 340.68 miles

Page 28: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 28 Department of ISM, University of Alabama, 1995-2002

Example 4: An insurance company collected data to estimate the mean value of personal property held by apartment renters in Tuscaloosa. In a random sample of 45 renters, the average value of personal property was $14,280 and the standard deviation was $6,540.

Example 4:

Page 29: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 29 Department of ISM, University of Alabama, 1995-2002

a. At 95% confidence, find the margin of error for estimating the true population mean?

Example 4:

t(.025,44) = 2.015m.o.e. = 1964.833

Page 30: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 30 Department of ISM, University of Alabama, 1995-2002

b. Construct a 95% confidence interval for the true mean value of personal property owned by renters in Tuscaloosa.

Example 4:

( 12,315, 16,245)

Page 31: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 31 Department of ISM, University of Alabama, 1995-2002

c. Three years ago the true mean value of personal property owned by renters in Tuscaloosa was $13,050.

Based on your confidence interval,is there evidence that the true mean has changed?

Example 4:

Page 32: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 32 Department of ISM, University of Alabama, 1995-2002

m.o.e. =

= 2.602 10 4

= 6.505

t sn

2 ,n-1

Find the “margin of error” at 98% confidence for estimating the mean gallons of water used to wash cars using 16 observations from a normal population if the sample standard deviation is calculated to be 10.0.

Page 33: M32 Margin of Error 1 Department of ISM, University of Alabama, 1995-2002 Lesson Objectives Learn the meaning of “margin of error,” or “m.o.e.” Learn.

M32 Margin of Error 33 Department of ISM, University of Alabama, 1995-2002

Definition

A (1– ) 100% confidence interval for

X + t / 2, n–1 sX

X + m.o.e.or

when is unknown and X ~ Normal, i.e., either original pop. ~ Normal or by CLT if n > 30,

is given bym.o.e.


KPMG Transport Tracker€¦ · MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN. Market fundamentals . Share prices (end of October

KPMG Transport Tracker€¦ · MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN. Market fundamentals . Share prices (end of October

& Conducted June 6 - 8, 1999 N=1,002 Registered “Likely” Voters Nationwide, With A +3.1% Margin Of Error.

& Conducted June 6 - 8, 1999 N=1,002 Registered “Likely” Voters Nationwide, With A +3.1% Margin Of Error.

Chapter 8: Estimating with Confidence the three steps for choosing a sample size for a desired margin of error when estimating . 5. What happens to the margin of error as z* gets smaller?

Chapter 8: Estimating with Confidence the three steps for choosing a sample size for a desired margin of error when estimating . 5. What happens to the margin of error as z* gets smaller?

SELECTED SOCIAL CHARACTERISTICS 2018 American … · Subject Estimate Estimate Margin of Error Percent Percent Margin of Error SELECTED SOCIAL CHARACTERISTICS 2018 American Community

SELECTED SOCIAL CHARACTERISTICS 2018 American … · Subject Estimate Estimate Margin of Error Percent Percent Margin of Error SELECTED SOCIAL CHARACTERISTICS 2018 American Community

A 'ij,. C?? t error, miscommunications have the potential of narrowing the margin ... etc.) and 2,790 requests for information, salutations, etc.

A 'ij,. C?? t error, miscommunications have the potential of narrowing the margin ... etc.) and 2,790 requests for information, salutations, etc.

CROP MARKS MARGIN The Wheely Big Cycle route map · MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN. North Route South Route .

CROP MARKS MARGIN The Wheely Big Cycle route map · MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN. North Route South Route .

'Margin of Error' in Property Valuations – is There a Need ...fig.net/.../papers/ts01f/TS01F_hiironen_niukkanen_et_al_6819.pdf · 'Margin of Error' in Property Valuations – Is

'Margin of Error' in Property Valuations – is There a Need ...fig.net/.../papers/ts01f/TS01F_hiironen_niukkanen_et_al_6819.pdf · 'Margin of Error' in Property Valuations – Is

Confidence interval and margin of error

Confidence interval and margin of error

Confidence intervals for Proportions Chapter 19. Objectives: 1.Standard Error 2.Confidence Interval 3.One-proportion z-interval 4.Margin of Error 5.Critical.

Confidence intervals for Proportions Chapter 19. Objectives: 1.Standard Error 2.Confidence Interval 3.One-proportion z-interval 4.Margin of Error 5.Critical.

1,000 Interviews Margin of Error: 3% Survey of Remittance Senders: U.S. to Latin America.

1,000 Interviews Margin of Error: 3% Survey of Remittance Senders: U.S. to Latin America.

Simulation for Examining Margin of Error and Sample Size: Binomial Proportions

Simulation for Examining Margin of Error and Sample Size: Binomial Proportions

CROP MARKS MARGIN MARGIN Fra MARGIN … CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN Fraud Barometer 2018 | 5 The national picture nd

CROP MARKS MARGIN MARGIN Fra MARGIN … CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN Fraud Barometer 2018 | 5 The national picture nd

& Conducted August 23-25, 1998 N=1,000 “Likely” Registered Voters Nationwide, With A +3.1% Margin Of Error.

& Conducted August 23-25, 1998 N=1,000 “Likely” Registered Voters Nationwide, With A +3.1% Margin Of Error.

Generalization error for multi-class margin classification

Generalization error for multi-class margin classification

700 Interviews, Conducted October 29 – November 1, 2009 Margin of error: +/- 3.7% Consumer Confidence Poll – Nov. 2009.

700 Interviews, Conducted October 29 – November 1, 2009 Margin of error: +/- 3.7% Consumer Confidence Poll – Nov. 2009.

KM C754e-20180129152033€¦ · 08/02/2018  · A Confidence Interval for a parameter has 2 parts : "estimate ± margin of error" b) Define margin of error: ho 0.0 close 40 be PL.

KM C754e-20180129152033€¦ · 08/02/2018  · A Confidence Interval for a parameter has 2 parts : "estimate ± margin of error" b) Define margin of error: ho 0.0 close 40 be PL.

Margin of Error and the Interval Estimate Interval ...

Margin of Error and the Interval Estimate Interval ...

TANet VoIPv4/v6 service Computer Center of M.O.E APAN29 VoIP WG.

TANet VoIPv4/v6 service Computer Center of M.O.E APAN29 VoIP WG.

The Future of Defence · 0 MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN The future of defence. Throughout this document, “we”,

The Future of Defence · 0 MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN The future of defence. Throughout this document, “we”,

Communicating Quantitative Information Inflation Election district Polling, predictions, confidence intervals, margin of error Homework: Identify topic.

Communicating Quantitative Information Inflation Election district Polling, predictions, confidence intervals, margin of error Homework: Identify topic.