Question

the eastern and western major league soccer conferences have a new reserve division that allows new players to develop their skills. data for a randomly picked date showed the following annual goals.

western eastern
los angeles 9 d.c. united 9
fc dallas 3 chicago 8
chivas usa 4 columbus 7
real salt lake 3 new england 6
colorado 4 metrostars 5
san jose 4 kansas city 3
table 10.25
the exact distribution for the hypothesis test is:

a. the normal distribution
b. the students t - distribution
c. the uniform distribution
d. the exponential distribution

Explanation:

When comparing two small - sample groups (in this case, the Eastern and Western Major League Soccer conferences' goal data) and the population standard deviation is unknown, the Student's t - distribution is appropriate for hypothesis testing. The normal distribution is used when the population standard deviation is known or for large samples. The uniform distribution is for equally likely outcomes over an interval. The exponential distribution is for the time between events in a Poisson process. Since we are dealing with two small samples and unknown population variances, the Student's t - distribution is the correct choice.

Answer:

B. the Student's t - distribution