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

Convenience sampling, Convenience Sampling It means a convenient sample...

Convenience Sampling It means a convenient sample is obtained by selecting convents units from the universe. Convenient sample is also known as chunk. It   means a fraction of

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

#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

Risk of portfolios, Risk of Portfolios So far, we have seen the applic...

Risk of Portfolios So far, we have seen the application of standard deviation in the context of risk in single investment. But usually most investors hold portfolios of securi

Median, Median Median is a position average. It is the value of middle ...

Median Median is a position average. It is the value of middle item of a variable when the items are arranged according to their values either in ascending or descending order.

Descriptive statistics, Descriptive Statistics : Carrying out an extens...

Descriptive Statistics : Carrying out an extensive analysis the data was not a subject to ambiguity and there were no missing values.  Below are descriptive statistics that hav

Disadvantages of median, Disadvantages For calculating median it is ...

Disadvantages For calculating median it is necessary to arrange the data; other averages do not need any arrangement. Since it is a positional average, its value is not d

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