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
Example: Write down the equation of the line which passes through the two points (-2, 4) and (3, -5). Solution At first glance it might not appear which we'll be capable to

a) Complete the inventory record below for an FOQ of 100 units. b) Talk about weaknesses of MRP. List at least 3 and describe each in a sentence or two. Item: A

Sequences Let us start off this section along with a discussion of just what a sequence is. A sequence is nothing much more than a list of numbers written in a particular orde

write each fraction as a decimal .round to the nearest hundredth if necessary (1-4) (14-21)


Calculate the value of the following limits. Solution From the graph of this function illustrated below, We can illustrate that both of the one-sided limits suffer

Suppose we are required to find the difference between 3abc and 7abc. We look at two scenarios. The value we would obtain by subtracting a larger quantity from th

Describe Adding and Subtracting Fractions in details? To add or subtract fractions, here are some steps: 1. Find the lowest common denominator (LCD) or any common denominato


The perimeter of Andrew''s rectangular room is 44 feet. What equation was used to find the perimeter?