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

Arithmetic mean, Arithmetic Mean   The process of computing Arithmetic M...

Arithmetic Mean   The process of computing Arithmetic Mean in the case of individual observations is to take the sum of the values of the variable and then divide by the number

Statistics to support learning, Scenario: Many of the years 5 and year 6 l...

Scenario: Many of the years 5 and year 6 learners' at Woodlands Park School were excited about being chosen for the cross-country team.  Every day, they were able to run laps of t

student is chosen randomly, In a management class of 100 childerns' 3 lang...

In a management class of 100 childerns' 3 languages are offered as an additional subject viz. Hindi, English and Kannada. There are 28 childrens taking Hindi, 26 taking Hindi and 1

Cluster analysis, These techniques are applied when the rows and the column...

These techniques are applied when the rows and the columns of the data table represent the same units and when the measure is a disiance or a similarity. The goal of the analysis i

Draw a network diagram for this problem, The project of building a backyard...

The project of building a backyard swimming pool consists of eight major activities and has to be completed within 19 weeks. The activities and related data are given in the follow

Asymmetric proximity matrices, Asymmetric proximity matrices Immediacy...

Asymmetric proximity matrices Immediacy matrices in which the off-diagonal elements which are, in the i th row and j th column and the j th row and i th column, are not essent

Cluster analysis, Cluster Analysis could be also represented more formally ...

Cluster Analysis could be also represented more formally as optimization procedure, which tries to minimize the Residual Sum of Squares objective function: where μ(ωk) - is a centr

Standard deviation , Standard Deviation  The concept of standard deviat...

Standard Deviation  The concept of standard deviation was first introduced by Karl Pearson in 1893. The standard deviation is the most important and the popular measure of disp

Compute a correlation coefficient, A researcher was interested lowering the...

A researcher was interested lowering the high school dropout level in his county. He measured the reading level of students entering middle school (based on a standard test) and th

Calculate the current ratio and quick ratio, You were recently hired by E&T...

You were recently hired by E&T Boats, Inc. to assist the company with its financial planning and to evaluate the company's performance.  E&T Boats, Inc. builds and sells boats to o

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