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

Determine that the events are mutually exclusive or not, In a study of outc...

In a study of outcomes for patients who had been in the Intensive care Unit (ICU) at a large hospital, the records from last 150 patients who had been in the ICU for more than one

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

Find the backward induction equilibrium, A rightist incumbent (player I) an...

A rightist incumbent (player I) and a leftist challenger (player C) run for senate. Each candidate chooses among two possible political platforms: Left or Right. The rules of the g

Analysis of variance (anova), Analysis of variance allows us to test whethe...

Analysis of variance allows us to test whether the differences among more than two sample means are significant or not. This technique overcomes the drawback of the method used in

WEDGE FRICTION, Ask question #MinimumA wedge is small piece of material hav...

Ask question #MinimumA wedge is small piece of material having two of their opposite faces not parallel. To lift block of weight W, it is pushed by horizontal force P which lifts t

Harmonic mean, The Harmonic Mean is based on the reciprocals of numbers ave...

The Harmonic Mean is based on the reciprocals of numbers averaged. It is defined as the reciprocal of the arithmetic mean of the reciprocal of the given individual observations. Th

Statistical inquiry, Main stages of Statistical Inquiry The following a...

Main stages of Statistical Inquiry The following are the various stages of a statistical inquiry (1)   Planning the Inquiry: First of all we have to assess the problem und

Predict higpa using a logistic regression, In this problem, we use the CSDA...

In this problem, we use the CSDATA data set, which is available in 'CSDATA.txt'. We do ne an indicator variable, say HIGPA, to be 1 if the GPA is 3.0 or better and 0 other- wise. S

Statistics, Theories of Business forecasting

Theories of Business forecasting

Business staitistices- soltion to :, A file on DocDepot in the assignments ...

A file on DocDepot in the assignments folder on doc-depot called bmi.mtp contains data on the Body Mass Index (BMI) of a population of Ottawa residents. The first column identifies

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