Eight golfers took part in an experiment in which they hit two different brands of golf balls. The table shows the distance traveled by each brand of ball (a table with three rows and eight columns is shown). How many degrees of freedom will there be in a t test to determine which brand of golf ball travels farthest?
There will be 14 degrees of freedom in a t test to determine which brand of golf ball travels farthest.
To calculate degrees of freedom for an independent samples t test, we use the formula:
df = (n1 - 1) + (n2 - 1)
where n1 and n2 are the sample sizes for each group being compared.
In this case, there were 8 golfers who hit two different brands of golf balls. This means that there were two groups, each with a sample size of 8.
So, using the formula above, we get:
df = (8 - 1) + (8 - 1) = 14
To determine the degrees of freedom in a t test, we need to consider the sample size of each group being compared. In this case, we have two different brands of golf balls and eight golfers.
For a t test comparing two groups, the degrees of freedom can be calculated using the formula:
degrees of freedom = n1 + n2 - 2,
where n1 and n2 represent the sample sizes of the two groups being compared.
Since we have eight golfers in total, and we are comparing two different brands of golf balls, the degrees of freedom for the t test would be:
degrees of freedom = 8 + 8 - 2,
degrees of freedom = 16 - 2,
degrees of freedom = 14.
Therefore, there will be 14 degrees of freedom in the t test to determine which brand of golf ball travels farthest.