Question

We will test whether the number of hours spent on practice is the same for football players as for basketball players.  A sample of 9 basketball players averages 2 hours per day of practice with a sample standard deviation of 0.866. A sample of 16 football players averages 3.2 hours per day of practice with a sample standard deviation of 1.0. Each population has a normal distribution. Use a 2 tail test. Are the numbers equal or not using alpha equals 0.05?

What is the simplified degrees of freedom?

What are the rejection regions?

What is the absolute value of the test statistic?

Answer 1

Let µ1 be the average hours per day of practice for basketball players.

Let µ2 be the average hours per day of practice for football players.

Claim : The number of hours spent on practice is the same for football players as for basketball players.

= vs ≠     

Assume σ²₁ ≠ σ²₂

Degrees of freedom = n1+n2-2

= 9+16-2

df = 23

Rejection region :

given α =0.05 , as H_a contain ≠  sign , this is two tail test.

Therefore critical value for two tail area t( 0.05 , 23 ) = 2.069 ----( from t distribution table )

Reject H0, if | t | ≥ 2.069 OR fail to reject H0, if | t | < 2.069

Given : = 2 , = 0.866 ,n₁ = 9 and   = 3.2 ,= 1 ,  n₂ = 16

Pooled estimate of standard deviaion :

S =

=

S = 0.9555

Test statistic:

t =

=  

= -1.2 / 0.3981

t = -3.01

Decision : | t | = 3.01

As | t | is greater than 2.069, we reject the null hypothesis H0

Conclusion : There is significant evidence that the number of hours spent on practice is the different for football players as for basketball players.