Two independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n1 - 25 and n2-35. The correct distribution to use is the 1) t distribution with 59 degrees of freedom 2) t distribution with 58 degrees of freedom. 3) t distribution with 61 degrees of freedom. 4) t distribution with 60 degrees of freedom e in tne abintres of students enroled n staustucs today if there is any diffe statistics teacher wants to see and those enrolled five years ago.



Answer :

2- T-distribution with 58 degrees of freedom

When the estimated standard deviation rather than the actual standard deviation is used as the denominator, the t-distribution is a continuous probability distribution of the z-score.

The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. If there is a remaining requirement for the data sample, particular data sample items must be picked after the degree of freedom quantity has been decided.

[tex]t[/tex] = Student's t-distribution

[tex]X{i}[/tex] = sample mean

μ = population mean

[tex]s[/tex] = sample standard deviation

[tex]n[/tex] = sample size

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