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

Carry out a t-test, Suppose that before the minimum wage law change, the un...

Suppose that before the minimum wage law change, the underlying mean number of part-time employees per Burger King Restaurant in New Jersey was 20.3. It was thought that the increa

Test for equality of two means, Let X 1  and X 2  be two independent po...

Let X 1  and X 2  be two independent populations with population means μ 1  and  μ 2  respectively. Two samples are taken, one from each population, of sizes n 1  and n 2  re

Median for ungrouped data, If the data set contains an odd number of items,...

If the data set contains an odd number of items, the middle item of the array is the median. If there is an even number of items, the median is the average of the two items. If the

Simple regression, Simple Regression: The Teacher Preparation Researc...

Simple Regression: The Teacher Preparation Research Team conducted a study of college students who took the Praxis II-a teacher certification examination. Some variables from

Small sample test for mean, If the sample size is less than 30, then we nee...

If the sample size is less than 30, then we need to make the assumption that X (the volume of liquid in any cup) is normally distributed. This forces    (the mean volume in the sam

Calculate the line of best fit, The manager of Pizza Hut provides a deliver...

The manager of Pizza Hut provides a delivery service for customers who telephone in an order. The manager would like to give callers an idea of the time it will take to deliver an

Pie diagram, Circles or Pie Diagram: Circles or pie diagrams are alter...

Circles or Pie Diagram: Circles or pie diagrams are alternative to squares. These are used  for the same purpose i.e. when  the values are differing  widely in their magnitude

Compute the sample mean and sample standard deviation, We want to investiga...

We want to investigate the income data.  In the Excel file Midterm  Data.xls there is a tab labeled "Income Data 2006".  The data in the tab is the income reported by 400 people in

., differance b/w big M mathod and two phase mathod

differance b/w big M mathod and two phase mathod

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