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

Plot diagnostic quantities, The data in the data frame compensation are fro...

The data in the data frame compensation are from Myers (1990), Classical andModern Regression with Applications (Second Edition)," Duxbury. The response y here is executive compens

What is the probability that they all hit the target, QUESTION ONE. (a) ...

QUESTION ONE. (a) The probability that, a bomber hits a target on a bombing mission is 0.70 Three bombers are sent to bomb a particular target. (i) What is the probability

Muti linear regression model problem, Muti linear regression model problem ...

Muti linear regression model problem An investigator is studying the relationship between weight (in pounds) and height (in inches) using data from a sample of 126 high school

Correlation, Correlation The board of directors of Bata Company is face...

Correlation The board of directors of Bata Company is faced with the problem of estimating what the annual sales might be in a shop to be opened in Bagpur where Bata has not op

Statistical definition of probability, Statistical Definition of probabilit...

Statistical Definition of probability: Ques: (a) (i)  Distinguish Statistical Definition of probability from the Classical Definition.                  (ii) State the A

Diversity of data , The box plot displays the diversity of data for the tot...

The box plot displays the diversity of data for the totexp; the data ranges from 30 being the minimum value and 390 being the maximum value. The box plot is positively skewed at 1.

Inferential Statistics.., A researcher computed the F ratio for a four-grou...

A researcher computed the F ratio for a four-group experiment. The computed F is 4.86. The degrees of freedom are 3 for the numerator and 16 for the denominator. 1. Is the computed

Probability, Ask queFrom these studies, which of the following may be consi...

Ask queFrom these studies, which of the following may be considered a variable that can have a probability distribution? [I] Percentage of Sub-Saharan Africans that smoke [II] Perc

Large sample test for mean, Large Sample Test for Mean A random sample ...

Large Sample Test for Mean A random sample of size n (n > 30) has a sample mean    . To test the hypothesis that the population mean μ has a specified value  μ 0  let us formu

Probability of remaining paint free, In a three-cornered paint ball duel, A...

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. The three paint ballers have different probabiliti

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