If the standard deviation for lifetimes of vacuum cleaners is estimated to be 400 hours, how large a sample must be taken in order to be 93% confident that the marge of error will not exceed 50 hours?

I know that n+(za/2)2 standard devation squared/the margin of error squared. What I don't know is how do I get the 93% confidence which is the z a/2 squared

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Posted on Jan 02, 2017

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I'm assuming here that 1,040 means one thousand and forty, not a metric decimal comma.

First we need the Std Dev of the mean value itself. This is

s / sqrt (n) = 21000 / sqrt (1040) = 651.2

Then the confidence interval for the mean value is

mean value ± Z * ( s / sqrt (n) )

where Z is an estimator related to the required confide

CL Z

99% 2.576

98% 2.326

95% 1.96

90% 1.645

So for a confidence of 95% the margin of error for the true value of the mean is

46239 ± 1.96 * 651.2 or

46239 ± 1276.3

that is, the mean of a sample from this process will be in this range to 95% confidence.

The margin of error for a future sample value would be

46239 ± 1.96 * 21000 or

46239 ± 41160

that is, a single sample value from this process will be in this range to 95% confidence.

.

First we need the Std Dev of the mean value itself. This is

s / sqrt (n) = 21000 / sqrt (1040) = 651.2

Then the confidence interval for the mean value is

mean value ± Z * ( s / sqrt (n) )

where Z is an estimator related to the required confide

CL Z

99% 2.576

98% 2.326

95% 1.96

90% 1.645

So for a confidence of 95% the margin of error for the true value of the mean is

46239 ± 1.96 * 651.2 or

46239 ± 1276.3

that is, the mean of a sample from this process will be in this range to 95% confidence.

The margin of error for a future sample value would be

46239 ± 1.96 * 21000 or

46239 ± 41160

that is, a single sample value from this process will be in this range to 95% confidence.

.

Jan 05, 2017 | Office Equipment & Supplies

First you need the Std Error of the mean value, a measure of the dispersion of that mean value.

SE = sample std deviation / sqrt (sample size)

= 100 / sqrt (64)

= 100 / 8

= 12.5

Then we use a figure for the number of std errors either side of the mean value, which make up a 95 % confidence interval. This is ± 1.96 std errors, from tables of the Normal Distribution.

So the confidence interval is

350 ± 1.96 * 12.5 or

374.5 to 325.5

.

SE = sample std deviation / sqrt (sample size)

= 100 / sqrt (64)

= 100 / 8

= 12.5

Then we use a figure for the number of std errors either side of the mean value, which make up a 95 % confidence interval. This is ± 1.96 std errors, from tables of the Normal Distribution.

So the confidence interval is

350 ± 1.96 * 12.5 or

374.5 to 325.5

.

Dec 11, 2015 | Institute of Mathematics and Statistics...

First you need the Std Error of the mean value, a measure of the dispersion of that mean value.

SE = sample std deviation / sqrt (sample size)

= 8 / ? 64

= 1

Then we use a figure for the number of std errors either side of the mean value, which make up a 99 % confidence interval. This is ± 2.58 std errors, from tables of the Normal Distribution.

So the confidence interval is

125 ± 2.58 * 1 or

127.58 to 122.42

.

SE = sample std deviation / sqrt (sample size)

= 8 / ? 64

= 1

Then we use a figure for the number of std errors either side of the mean value, which make up a 99 % confidence interval. This is ± 2.58 std errors, from tables of the Normal Distribution.

So the confidence interval is

125 ± 2.58 * 1 or

127.58 to 122.42

.

Dec 10, 2015 | Institute of Mathematics and Statistics...

Manual is available in PDF format from here

http://docslide.us/download/link/dca-operators-guide

http://docslide.us/download/document/?id=%2FJKJQj2KkZIjS9Tn4Jm5CAbRibVv%2BGl%2BT9wi7I03ZyGSjZf8c1bXQnPy2%2FSc3BFIu8t3mvccp4VXj23OQyX8pQ%3D%3D

DCA Vantage Operator's Guide 109

Troubleshooting

E22 - Optical

reading is out

of range

A Sample or Reference

channel reading taken

during an Air

measurement is too

high.

1. Discard the sample.

2. Run an optical test.

3. If you are unable to run an

optical test, contact your local

technical support provider.

E23 -

Excessive

noise on the

Sample

channel

The standard deviation

of the 16 readings at the

Sample channel for Dark

or Air reading is too

large.

1. Discard the sample.

2. Run an optical test.

3. If you are unable to run an

optical test, contact your local

technical support provider.

E24 -

Excessive

noise on the

Reference

channel

The standard deviation

of the 16 readings at the

Reference channel for

Dark, Air or Sample

reading is too large.

1. Discard the sample.

2. Run an optical test.

3. If you are unable to run an

optical test, contact your local

technical support provider.

E26 -

Excessive

noise in sample

reading

The standard deviation

of the 16 readings at the

Sample channel during a

reading taken is too

large in Sample read

position.

1. Discard the sample.

2. Run an optical test.

3. If you are unable to run an

optical test, contact your local

technical support provider.

E27 -

Excessive

Lamp Drift

The change in mean

signal between

successive Air readings

is too large at either the

Sample channel or the

Reference channel.

1. Discard the sample.

2. Run an optical test.

3. If you are unable to run an

optical test, contact your local

technical support provider.

E30 - Thermal

control system

error - low

The temperature

measured by one of the

cartridge holder

thermistors is ?2?C.

1. Discard the sample.

2. Restart the system.

3. If you are unable to perform a

successful restart, contact

your local technical support

provider.

E

http://docslide.us/download/link/dca-operators-guide

http://docslide.us/download/document/?id=%2FJKJQj2KkZIjS9Tn4Jm5CAbRibVv%2BGl%2BT9wi7I03ZyGSjZf8c1bXQnPy2%2FSc3BFIu8t3mvccp4VXj23OQyX8pQ%3D%3D

DCA Vantage Operator's Guide 109

Troubleshooting

E22 - Optical

reading is out

of range

A Sample or Reference

channel reading taken

during an Air

measurement is too

high.

1. Discard the sample.

2. Run an optical test.

3. If you are unable to run an

optical test, contact your local

technical support provider.

E23 -

Excessive

noise on the

Sample

channel

The standard deviation

of the 16 readings at the

Sample channel for Dark

or Air reading is too

large.

1. Discard the sample.

2. Run an optical test.

3. If you are unable to run an

optical test, contact your local

technical support provider.

E24 -

Excessive

noise on the

Reference

channel

The standard deviation

of the 16 readings at the

Reference channel for

Dark, Air or Sample

reading is too large.

1. Discard the sample.

2. Run an optical test.

3. If you are unable to run an

optical test, contact your local

technical support provider.

E26 -

Excessive

noise in sample

reading

The standard deviation

of the 16 readings at the

Sample channel during a

reading taken is too

large in Sample read

position.

1. Discard the sample.

2. Run an optical test.

3. If you are unable to run an

optical test, contact your local

technical support provider.

E27 -

Excessive

Lamp Drift

The change in mean

signal between

successive Air readings

is too large at either the

Sample channel or the

Reference channel.

1. Discard the sample.

2. Run an optical test.

3. If you are unable to run an

optical test, contact your local

technical support provider.

E30 - Thermal

control system

error - low

The temperature

measured by one of the

cartridge holder

thermistors is ?2?C.

1. Discard the sample.

2. Restart the system.

3. If you are unable to perform a

successful restart, contact

your local technical support

provider.

E

Sep 21, 2015 | Siemens Dishwashers

The standard deviation is a measure of how "tight" the samples are distributed around your mean.

In layman's terms, a small standard deviation indicates that most of your measurements are in the vicinity of the means; a large standard deviation corresponds to readings that are all over the place.

You could also say that the smaller the SD, the more your mean is representative of the data set.

For a better explanation, just look up Standard deviation on Wikipedia!

In layman's terms, a small standard deviation indicates that most of your measurements are in the vicinity of the means; a large standard deviation corresponds to readings that are all over the place.

You could also say that the smaller the SD, the more your mean is representative of the data set.

For a better explanation, just look up Standard deviation on Wikipedia!

May 03, 2014 | Audio Players & Recorders

Population size:4

Mean (?): 23.45

Standard deviation (?): 4.5986411036305

Mean (?): 23.45

Standard deviation (?): 4.5986411036305

Mar 07, 2014 | Office Equipment & Supplies

Count the number of items in the sample whose statistics you're calculating. For example, if you're calculating the mean and standard deviation of five items then the sample size is five.

Apr 18, 2012 | Casio FX-9750GPlus Calculator

Count the number of items in the sample whose statistics you're calculating. For example, if you're calculating the mean and standard deviation of seven items then the sample size is seven.

Apr 18, 2012 | Casio FX-9750GPlus Calculator

At 95% confidence level the limits are 57.47 -1.96*1.3 and 57.47+1.96*1.3. so there is no reason to reject the hypothesis

Jan 02, 2011 | Computers & Internet

34 σ+

39 σ+

32 σ+

36 σ+

30 σ+

33 σ+

2nd ÷ (σxn)

39 σ+

32 σ+

36 σ+

30 σ+

33 σ+

2nd ÷ (σxn)

Jun 02, 2009 | Texas Instruments TI-30XA Calculator

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