Test of hypothesis about the population mean, Mathematics

Test of hypothesis about the population mean

When the population standard deviation (S) is identified then the t statistic is defined as

            t = ¦(x¯ - µ)/ S¦        whereas: S = s/√n

Follows the students t distribution along with (n-1) d.f. whereas

      x¯ = Sample mean

      μ = Hypothesis population mean

      n = sample size

And S is the standard deviation of the sample calculated though the formula

S=607_Test of hypothesis about the population mean.png

 

for n < 30

If the calculated value of t exceeds the table value of t at a particular level of significance, the null hypothesis is rejected.

Illustration

Ten oil tins are taken at random from an automatic filling machine. The mean weight of the tins is 15.8 kilogram (kg) and the standard deviation is 0.5 kilogram (kg). Does the sample mean differ significantly from the intended weight of 16 kilogram (kg). Use 5 percent level of significance.

Solution

Described that n = 10;   x¯= 15.8; S = 0.50; μ = 16; v = 9

      H0: μ = 16

      H1: μ ≠ 16

            = 

t = ¦ {(15.8 - 16)/(0.5/√10)}¦

      = ¦{0.2/0.16}¦

      = -1.25

The table value for t for 9 d.f. at 5 percent level of significance is 2.26. The computed value of t is smaller than the table value of t. hence, difference is insignificant and the null hypothesis is accepted.

Posted Date: 2/19/2013 1:40:55 AM | Location : United States







Related Discussions:- Test of hypothesis about the population mean, Assignment Help, Ask Question on Test of hypothesis about the population mean, Get Answer, Expert's Help, Test of hypothesis about the population mean Discussions

Write discussion on Test of hypothesis about the population mean
Your posts are moderated
Related Questions
The angle of elevation of the top of a tower standing on a horizontal plane from a point A is α .After walking a distance d towards the foot of the tower the angle of elevation is


Non Linear Relationships If the correlation coefficient and the scatter diagram do not indicate linear relationship, then the relationship may be nonlinear. Two such relations

darien agrees to sponsor her sister $8 plus $1 for every mile she walks.Write an expression to show her total money

Q. What are Mutually Exclusive events? Mutually Exclusive Events are mutually exclusive if they cannot occur at the same time. For example, if you roll one die, you canno

apllication in business and economics

what is the difference between North America''s part of the total population and Africa''s part

Integration Integration is the reversal of differentiation An integral can either be indefinite while it has no numerical value or may definite while have specific numerical v

Q. How to Left shifts and right shifts a graph? Ans. When you're translating (shifting) a graph, it's easy to get subtracting and adding mixed up. It seems counter-intuiti

If 28,000 = 85% and 28,000 / X = 100%. What the freak is X and how do you work it out.