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

Graphical calculation for mode, For calculating the mode of the grouped dat...

For calculating the mode of the grouped data graphically, the following procedure is adopted. Draw a histogram of the data; the modal class is the tallest rectangle.

Pneumatic actuator design matrix, Pneumatic Actuator Design Matrix: The ra...

Pneumatic Actuator Design Matrix: The range of actuator design parameters have been provisionally assessed and are presented in Table. You are required to determine the following

Normal curve applications, Replacement times for TV sets are normally distr...

Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. Find the replacement time that separates the top 20% from the

Standard gaussian random variable , You will recall the function pnorm() fr...

You will recall the function pnorm() from lectures. Using this, or otherwise, Dteremine the probability of a standard Gaussian random variable exceeding 1.3.  Using table(), or

Econometrics, Ask question From the household budget survey of 1980 of the...

Ask question From the household budget survey of 1980 of the Dutch Central Bureau of Statistics, J. S. Cramer obtained the following logit model based on a sample of 2820 househol

Calculate the seasonal indexes , The total number of overtime hours (in 100...

The total number of overtime hours (in 1000s) worked in a large steel mill was recorded for 16 quarters, as shown below. Year Quarter Overtime hour

How many possible latin square designs are there, In an agricultural experi...

In an agricultural experiment, we wish to compare the yields of three different varieties of wheat. Call these varieties A, B and C. We have a ?eld that has been marked into a 3 *

Normal probability plots, The Null Hypothesis - H0:  The random errors will...

The Null Hypothesis - H0:  The random errors will be normally distributed The Alternative Hypothesis - H1:  The random errors are not normally distributed Reject H0: when P-v

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

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