Degrees Of Freedom Sample Size

Introduction to degrees of freedom sample size

In statistics hypothesis testing are used to compute the probability for a particular hypothesis to be right. Hypothesis is specified as declaration which may or may not be precise. In statistics two hypothesis testing are consumed. The number of degrees of freedom is specified as the number of independent observations within a sample of data to are obtainable to approximate a constraint of the population from which that sample is drawn. Let us see about the degrees of freedom sample size.

Degrees of Freedom Sample Size

The degrees of freedom are identifying as a function of both sample size and the number of independent variables.

The degrees of freedom are equivalent to the number of independent observations , otherwise the number of topics within the data, subtract the number of parameters estimated .

T test

't = (barx-mu)/(s/sqrt(n))' ~ t(n-1)

In the above T test has the (n-1) degrees of freedom.

Example

Consider the random sample of 35 students scored an average of 19 marks and sum of the squares of the deviation taken from the mean is 70.

In this example the random sample size n = 35

Therefore degrees of freedom = (n-1) = 35-1) = 34

Degrees of freedom = 34

Examples for Degrees of Freedom Sample Size

The average number of articles created by two machines per day 175 and 250 with standard deviation 20 and 25 correspondingly. On the basis of records of 25 day production can you regard both the machines are uniformly efficient at 1% level of significance.

Solution

Null hypothesis:

H0: Both the machines are equally efficient.

Test statistic:

t = '(bar x- bar y)/(ssqrt(1/n_(1)+1/n_(2)))'

Where ' s^n = (n_(1) s_(1)^2+n_(2)s_(2)^2)/(n_(1)+n_(2)-2)'

Level of significance:

a = 0.05 at 1% level for 48 degrees of freedom 't' table value is 2.01.

Calculation:

'barx '=175, 'bary '=250, n1 = n2=25, s1= 20, s2 = 25

' s^2 = (25xx400+25xx625)/(50-2)'

' s^2 = (45625/48)'

s2=533.8541

s= 23.105

t = '(175- 250)/(23.105sqrt(1/25+1/25))'

t = '(-75)/(23.105sqrt(0.08))'

t = '(-75)/(6.5340)'

t = 11.478

| t | = 11.478

Calculated value = 11.478

Table value = 2.0

Calculated value > table value

Null hypothesis is rejected

Result:

Both the machines are not equally sufficient.

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by: Omkar Nayak

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