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

Weighted arithmetic mean, Weighted Arithmetic Mean Another aspect...

Weighted Arithmetic Mean Another aspect to be considered is the importance we assign to each observation. The arithmetic mean as we calculated it so far gives equal

Probability, In 120 tosses of a coin, 45 heads and 75 tails are observed. ...

In 120 tosses of a coin, 45 heads and 75 tails are observed. Is this a balanced coin? Use a=0.05. (Follow the basic steps of hypothesis testing)

Correlation - cause and effect, Cause and Effect Even a highly signifi...

Cause and Effect Even a highly significant correlation does not necessarily mean that a cause and effect relationship exists between the two variables. Thus, correlation does

How many possible latin square designs are there, In an agricultural experi...

In an agricultural experiment, we wish to compare the yields of three different varieties of wheat. Call these varieties A, B and C. We have a ?eld that has been marked into a 3 *

Optimal number of cluster, Try different numbers of clusters in your progra...

Try different numbers of clusters in your program (K=2...15) and build a plot that shows the dependency between number K and value of RSS function on the last iteration. What is th

Disadvantages of mode, Disadvantages The value of mode cannot always...

Disadvantages The value of mode cannot always be determined. In some cases we may have a bimodal series. It is not capable of algebraic manipulations. For example, from t

Stream flow gauging, (a) At a stream gauging station, the following dischar...

(a) At a stream gauging station, the following discharges and stage measurements were taken for the purpose of the rating curve at that section: Stage (m) 1

Anova, how do you find if two way or one way

how do you find if two way or one way

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