Large sample test for mean, Applied Statistics

Assignment Help:

Large Sample Test for Mean

A random sample of size n (n > 30) has a sample mean   218_computation of covariance ungrouped data2.png . To test the hypothesis that the population mean μ has a specified value  μ0 let us formulate the Null Hypothesis as H0:   μ = μ0 .

The Alternative Hypothesis is (i) H1:    μ ≠ μ0   or (ii) H1:    μ > μ0   or (iii) H1:    μ < μ0  . Since n is large, the sampling distribution of  218_computation of covariance ungrouped data2.png   is approximately normal.

If H0 is true, the test statistic z =   911_large sample test for mean.png   has approximately a standard normal distribution. The critical region for z depending on the nature of H1 and level of significance  α is given below:

Level of significance ( α )

10%

5%

1%

Critical region for  μ ≠ μ0

  | z |   > 1.64

| z |  > 1.96

| z | >  2.58

Critical region for  μ > μ0

    z    < -1.28

   z   < -1.64

   z <  -2.33

Critical region for  μ < μ0 

    z    > 1.28

z > 1.64

  z >   2.33                                 


Related Discussions:- Large sample test for mean

Types of correlation, Type of Correlation 1.      Positive and Negat...

Type of Correlation 1.      Positive and Negative Correlation: 2.      Simple Partial and Multiple Correlations. 3.      Linear and  Non linear or Correlations

Bernoulli''s theorem, Bernoulli's Theorem If a trial of an experiment c...

Bernoulli's Theorem If a trial of an experiment can result in success  with probability p and failure with probability q (i.e.1-p) the probability of exactly r success in n tri

BMI, Identify the (time, censor) pair for each of the following analyses:

Identify the (time, censor) pair for each of the following analyses:

Asymmetric proximity matrices, Asymmetric proximity matrices Immediacy...

Asymmetric proximity matrices Immediacy matrices in which the off-diagonal elements which are, in the i th row and j th column and the j th row and i th column, are not essent

Arithmetic mean, Arithmetic Mean   The process of computing Arithmetic M...

Arithmetic Mean   The process of computing Arithmetic Mean in the case of individual observations is to take the sum of the values of the variable and then divide by the number

Determine the compressive force, The weight of the engine in kN is given in...

The weight of the engine in kN is given in P2 and is suspended from a vertical chain at A. A second chain round the engine is attached at A, with a spreader bar between B and C. Th

Quartiles, Related Positional Measures Besides median, there are other ...

Related Positional Measures Besides median, there are other measures which divide a series into equal parts. Important amongst these are quartiles, deciles and percentiles.

Confidence interval, for this proportion, use the +-2 rule of thumb to dete...

for this proportion, use the +-2 rule of thumb to determine the 95 percent confidence interval. when asked if they are satisfied with their financial situation, .29 said "very sat

Determine how the ordinary least squares, Question Following the general...

Question Following the general methodology used by econometricians as explained in the session for week 1 (eight steps), explain how you would proceed to determine if a good com

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