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

Significance of correlation, Significance of Correlation The study of c...

Significance of Correlation The study of correlation is of immense use in practical life. Correlation analysis contributes to the understanding of economic behavior, aids in lo

Regression lines, Regression Lines It has already been discussed that t...

Regression Lines It has already been discussed that there are two regression lines and they show mutual relationship between two variable . The regression line Yon X gives   th

Scenario- Superior Health Care System Inc., The management at Superior Heal...

The management at Superior Health Care System Incorporated recently purchased several new facilities including the central patient information management center. This purchase will

Time series, Measurement of trend , least square method

Measurement of trend , least square method

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

Compute a correlation coefficient, A researcher was interested lowering the...

A researcher was interested lowering the high school dropout level in his county. He measured the reading level of students entering middle school (based on a standard test) and th

Calculate the ratio of the sample standard deviation, The Case Study includ...

The Case Study included information about the price for a full meal before and after the law change (in dollars).  Of interest is whether the differences in price for a full meal b

Explain ridge regression, Using log(x1), log(x2) and log(x3) as the predict...

Using log(x1), log(x2) and log(x3) as the predictors, do pair wise scatterplots of all pairs of variables (including the response) and comment (use the pairs function). Do you thin

Finding the z-score, 10. If a set of scores has a sample mean of 25 and a s...

10. If a set of scores has a sample mean of 25 and a sample variance of 4, find the following: a. the z-score for a raw score of 31 b. the z-score for a raw score of 18 c. the raw

Regression Analysis, Question 3 25 marks Your employer, Quick Hit Agency ...

Question 3 25 marks Your employer, Quick Hit Agency (QHA), is a debt collections agency. The company specializes in collecting small accounts. QHA does not deal in large accounts

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