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

Decision theory, 1. Definition of decision tree, 2. Feature of decision the...

1. Definition of decision tree, 2. Feature of decision theory problem

Continuous frequency distribution, Formation of Continuous Frequency Distri...

Formation of Continuous Frequency Distribution:    Continuous frequency distribution is most popular in practice. With reference to the formation of this type of frequency distr

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

Purposive or judgement sampling, Purposive or Judgement Sampling Under ...

Purposive or Judgement Sampling Under this method of sampling, the choice  of selection of sample  items from the universe  depends exclusively on the judgement  of the investi

Probability, In 120 tosses of a coin, 45 heads and 75 tails are observed. ...

In 120 tosses of a coin, 45 heads and 75 tails are observed. Is this a balanced coin? Use a=0.05. (Follow the basic steps of hypothesis testing)

Correlation coefficient test, 1. If you are calculating a correlation coeff...

1. If you are calculating a correlation coefficient testing the relationship between height and weight, state the null and alternative hypotheses. 2. What kind of relationship d

Association of attributes, In an examination 600 candidates appeared, boys ...

In an examination 600 candidates appeared, boys outnumbered girls by 16% of all candidates. number of passed candidates exceeded the number of failed candidates by 310. Boys failin

Carry out a t-test, Suppose that before the minimum wage law change, the un...

Suppose that before the minimum wage law change, the underlying mean number of part-time employees per Burger King Restaurant in New Jersey was 20.3. It was thought that the increa

Type of variable in regression analysis, Type of Variable in Regression Ana...

Type of Variable in Regression Analysis There are two types of variable in regression analysis. These are: a.      Dependent variable b.      Independent variable

Caveat, Caveat We must be careful when interpreting the meaning of asso...

Caveat We must be careful when interpreting the meaning of association. Although two variables may be associated, this association does not imply that variation in the independ

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