Large samples, Mathematics

Assignment Help:

LARGE SAMPLES

These are samples that have a sample size greater than 30(that is n>30)

(a)   Estimation of population mean

Here we suppose that if we take a large sample from a population then the mean of the population is extremely close to the mean of the sample

Steps to follow to estimate the population mean having:

i.  Take a random sample of n items where (n>30)

ii.  Calculate sample mean (x¯) and standard deviation (S)

iii.  Calculate the standard error of the mean by using the following formular

 

S = s/√n

Whereas S= Standard error of mean

S = standard deviation of the sample

n = sample size

iv. Choose a confidence level for illustration: 95 percent or 99 percent

 

v. Estimate the population mean as under

 

Population mean µ = x¯ ± (Appropriate number) × S

'Appropriate number' means confidence level for illustration, at 95 percent confidence level is 1.96 this number is generally denoted by Z and is acquired from the normal tables.

Illustration

The quality department of a wire manufacturing company periodically chooses a sample of wire specimens in order to test for breaking strength. Past experience has displayed that the breaking strengths of a specific type of wire are normally distributed along with standard deviation of 200 kilogram (kg). A random sample of 64 specimens gave a mean of 6200 kilogram (kg). Find out the population mean at 95 percent level of confidence

Solution

Population mean = x¯ ± 1.96 S

Note that sample size is already n > 30 whereas s and are described hence step i), ii) and iv) are provided.

Now:  x¯ = 6200 kilogram (kg)

S= s/√n  = 200/√64 =  25

 

Population mean         = 6200 ± 1.96(25)

                                    = 6200 ± 49

                                    = 6151 to 6249

At 95 percent level of confidence, population mean will be in among 6151 and 6249

 


Related Discussions:- Large samples

Two circles touching internally prove that ox:oy=oa:ob, Two circles touchin...

Two circles touching internally at O. OXY, OAB straight lines, the latter passing through the centres. Prove that OX : OY = OA : OB. Given : Two circles touching internally a

Rules of game theory, Rules Of Game Theory i.   The number of competito...

Rules Of Game Theory i.   The number of competitors is finite ii.   There is conflict of interests among the participants iii.  Each of these participants has available t

Linear Programming, A garden shop wishes to prepare a supply of special fer...

A garden shop wishes to prepare a supply of special fertilizer at a minimal cost by mixing two fertilizers, A and B. The mixture is to contain at least 45 units of phosphate at lea

How to add mixed numbers, Q. How to Add Mixed Numbers? Ans. If you...

Q. How to Add Mixed Numbers? Ans. If you have to add mixed numbers, you might try this method first: First rewrite the mixed number as a whole number plus a fracti

Simplify Radicals, Can I have simplify radicals for Alebgera 2

Can I have simplify radicals for Alebgera 2

Hcf, the length of three pieces of ropes are 140cm,150cm and 200cm.what is ...

the length of three pieces of ropes are 140cm,150cm and 200cm.what is the greatest possible length to measure the given pieces of a rope?

Related to MCA, AskIf y=e^(a?sin?^(-1) x), prove that (1 – x2)yn+2 – (2n + ...

AskIf y=e^(a?sin?^(-1) x), prove that (1 – x2)yn+2 – (2n + 1)xyn+1 – (n2 + a2)yn = 0. Hence find the value of yn when x = 0. question #Minimum 100 words accepted#

Find the larger of two supplementary angles, The larger of two supplementar...

The larger of two supplementary angles exceeds the smaller by 180, find them. (Ans:990,810) Ans:    x + y = 180 0          x - y =  18 0        -----------------

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd