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

Determine market interest rate, The interest rate on the three year loan is...

The interest rate on the three year loan is 0.087. Whereas the interest rate on the two year loan is 0.085 as given in A. Suppose that the liquidity premium at t=1 is 0.002 and tha

Question with R - Bioinformatics, Hi There, I have a question regarding R,...

Hi There, I have a question regarding R, and I am wondering if anyone can help me. Here is a code that I would like to understand: squareFunc g f(x)^2 } return(g) } sin

Time series, merits and demerits of methods to determin trends

merits and demerits of methods to determin trends

Calculate the seasonal indexes , The total number of overtime hours (in 100...

The total number of overtime hours (in 1000s) worked in a large steel mill was recorded for 16 quarters, as shown below. Year Quarter Overtime hour

Types of averages, The following are the various types of common averages u...

The following are the various types of common averages used in statistical analysis given in the form of a chart. Figure 1

Assignment, wants to complete assignment for uk university which i need toy...

wants to complete assignment for uk university which i need toy submit latest by 10th october

#regression, #regression line drawn as Y=C+1075x, when x was 2, and y was 2...

#regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Geometric mean, Geometric Mean The geometric mean   of numbers is defin...

Geometric Mean The geometric mean   of numbers is defined as the th root of the product of numbers .It is obtained by multiplying all the values of a variable and then extracti

Factor loadings matrix, As we stated above, we start factor analysis with p...

As we stated above, we start factor analysis with principal component analysis, but we quickly diverge as we apply the a priori knowledge we brought to the problem. This knowled

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