Large sample test for proportion, Applied Statistics

Assignment Help:

Large Sample Test for Proportion

A random sample of size n (n > 30) has a sample proportion p of members possessing a certain attribute (success). To test the hypothesis that the proportion p in the population has a specified value p0.

The Null Hypothesis is H0: p = p0.

The Alternative Hypothesis is (i) H1: p ≠ por (ii) H1: p < p0, or (iii) H1: p > p0.

Since n is large, the sampling distribution of  1534_sampling.png  is approximately normal.

If H0 is true, the test statistic z =  931_large sample test.png  is approximately normally distributed.

The critical region for z depending on the nature of H1 and level of significance α is given in the following table:

Rejection Rule for H0: p = p0

Level of significance

10%

5%

1%

Critical region for p    p0

    | z |   >  1.64

   | z |     >   1.96

   | z |     >   2.58

Critical region for p < p0

       z    <   -1.28

     z       <   -1.64

     z      <  -2.33

Critical region for p > p0

      z    >   1.28

     z       >   1.64

     z      >  2.33                              


Related Discussions:- Large sample test for proportion

Find the minimum constant workforce, Find the minimum constant workforce: ...

Find the minimum constant workforce: ABC Company, a manufacturer of roofing supplies, has developed monthly forecasts for roofing tiles. The forecasted demand and the expected

Eliminate all of the insignificant variables, The file Midterm Data.xls ha...

The file Midterm Data.xls has a tab labeled "Many vs. S&P" which presents historical price data for several assets, a volatility condition (VIDX = 1 if the NYSE volatility is grea

Utility function, The decision maker ranks lotteries according to the utili...

The decision maker ranks lotteries according to the utility function (i) State the independence assumption. Does this decision maker satisfy it? (ii) Is this decision ma

Statistical keys, Statistical Keys To do statistical o...

Statistical Keys To do statistical operations we must first set the calculator on SD mode [SD stands for "standard deviation" which is the usual st

Binomial distribution, Binomial Distribution Binomial distribution  was...

Binomial Distribution Binomial distribution  was discovered by swiss mathematician James  Bernonulli, so this distribution is called as Bernoulli distribution also, this is a d

Harmonic mean, The Harmonic Mean is based on the reciprocals of numbers ave...

The Harmonic Mean is based on the reciprocals of numbers averaged. It is defined as the reciprocal of the arithmetic mean of the reciprocal of the given individual observations. Th

Interpolation and extrapolation, Meaning of Interpolation and Extrapolation...

Meaning of Interpolation and Extrapolation Interpolation is a method of estimating the most probable  missing figure on  the basis of given data under certain assumptions. On t

Harmonic mean, The Harmonic Mean is based on the reciprocals of numbers ave...

The Harmonic Mean is based on the reciprocals of numbers averaged. It is defined as the reciprocal of the arithmetic mean of the reciprocal of the given individual observations. Th

Admissibility, Admissibility A very common concept which is applicable ...

Admissibility A very common concept which is applicable to any procedure of the statistical inference. The underlying notion is that the procedure/method is admissible if and o

Stata question, i am new to stata and i am trying to figure out how to calc...

i am new to stata and i am trying to figure out how to calculate expected growth of sales tax revenue as well as average growth rate of sales tax revenue in stata. I have a dataset

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