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

Postneonatal mortality rate, Mid year population 440000 Late fatal death...

Mid year population 440000 Late fatal death          29 No. of live birth           5200 No. of infant death      423 No. of maternal death 89 No. of infant deaths i

MEASURING TREND, DISCUSS THE METHODS OF MEASURING TREND

DISCUSS THE METHODS OF MEASURING TREND

Standard deviation for grouped data, Grouped data  For ...

Grouped data  For grouped data, the formula applied is  σ = Where f = frequency of the variable, μ= population mea

Find the optimal adaptive meshes for a skewed beta density, Show that the I...

Show that the ISB in a bin containing the origin of the double exponen-tial density, f(x) = exp(-|x|)/2, is O(h 3 ); hence, the discontinuity in the derivative of f does not have a

Inference on reggression analysis, find the expected value of the mean squa...

find the expected value of the mean square error and of the mean square reggression

Half of market share, Your company has developed a new product .Your compan...

Your company has developed a new product .Your company is a reputed company with 50% market share of same range of products. Your competitors also come with their new products equa

Arithmetic average or mean, Arithmetic Average or Mean The arithmetic m...

Arithmetic Average or Mean The arithmetic mean is the most widely and the most generally understandable of all the averages. This is clear from the reason that when the term

Circul;atory ststistics Lab, What statistics can be obtained from a circula...

What statistics can be obtained from a circulatory lab?

Probability, HOW WOULD YOU INTERPRET THIS PROBABILITY:P(a)=1.05

HOW WOULD YOU INTERPRET THIS PROBABILITY:P(a)=1.05

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