Determine the number of degrees of freedom for the two-sample t test or ci in each of the following situations. (round your answers down to the nearest whole number.)

(a) m = 12, n = 10, s1 = 4.0, s2 = 5.0
(b) m = 12, n = 15, s1 = 4.0, s2 = 5.0
(c) m = 12, n = 15, s1 = 3.0, s2 = 5.0
(d) m = 10, n = 24, s1 = 4.0, s2 = 5.0

(a) m = 12, n = 10, s1 = 4.0, s2 = 5.0

(equal variances)

 (Assuming unequal variances)

(b) m = 12, n = 15, s1 = 4.0, s2 = 5.0

(equal variances)

 (Assuming unequal variances)

(c) m = 12, n = 15, s1 = 3.0, s2 = 5.0

(equal variances)

 (Assuming unequal variances)

(d) m = 10, n = 24, s1 = 4.0, s2 = 5.0

(equal variances)

 (Assuming unequal variances)

Step-by-step explanation:

1) Previous concepts

The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.

The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."

And if we have two sample of size m and n from two independet samples the correct formula for the degrees of freedom is:

(Assuming equal variances)

 (Assuming unequal variances)

2) Solution to the problem

Using this formula we can answer all the cases:

(a) m = 12, n = 10, s1 = 4.0, s2 = 5.0

(equal variances)

 (Assuming unequal variances)

(b) m = 12, n = 15, s1 = 4.0, s2 = 5.0

(equal variances)

 (Assuming unequal variances)

(c) m = 12, n = 15, s1 = 3.0, s2 = 5.0

(equal variances)

 (Assuming unequal variances)

(d) m = 10, n = 24, s1 = 4.0, s2 = 5.0

(equal variances)

 (Assuming unequal variances)