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

Limitations of arithmetic mean, The calculations of arithmetic mean m...

The calculations of arithmetic mean may be simple and foolproof, but the application of the result may not be so foolproof. An arithmetic mean may not merely lack

Estimation, what do we mean by critical region

what do we mean by critical region

BIVARIATE FREQUENCY , MARKS IN LAW :10 11 10 11 11 14 12 12 13 10 MARKS IN ...

MARKS IN LAW :10 11 10 11 11 14 12 12 13 10 MARKS IN STATISTICS :20 21 22 21 23 23 22 21 24 23 MARKS IN LAW:13 12 11 12 10 14 14 12 13 10 MARKS IN STATISTICS:24 23 22 23 22 22 24 2

Measures of dispersion, Measures of Dispersion ...

Measures of Dispersion Box 3: Food vs. Oil Below are the figures for foodgrain procurement   and cr

Spatial ability test, What would be the cutoff score to indicate a score th...

What would be the cutoff score to indicate a score that is in the top 15% of the scores on a test with a mean of 100 and a standard deviation of 15? This question has multiple p

ANOVA, Your company operates a machine shop, and, having heard you had expe...

Your company operates a machine shop, and, having heard you had experience in statistics and design of experiments, consulted you for your opinion on an experiment they want to run

Purposive or judgement sampling, Purposive or Judgement Sampling Under ...

Purposive or Judgement Sampling Under this method of sampling, the choice  of selection of sample  items from the universe  depends exclusively on the judgement  of the investi

Multiple regression analysis, Complete the multiple regression model using ...

Complete the multiple regression model using Y and your combined X variables.  State the equation.  Next, make sure that you evaluate overall model performance with the Anova table

Find probability of remaining paint free - ball duel, In a three-cornered p...

In a three-cornered paint ball duel, A, B, and C successively take shots at each other until only one of them remains paint free. Once hit, a player is out of the game and gets no

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