Question

In 2000, the average GPA for Rutgers College students was 3.15. A sample in 2002 showed that the average GPA for Rutgers College students was 3.46.
An alternative hypothesis for the GPA of Rutgers College students is:

A. The mean Rutgers College GPA is more than 3.15 and less than 3.46
B. The mean Rutgers College GPA is less than 3.46
C. The mean Rutgers College GPA has increased to more than 3.15
D. None of the above

Answer 1

Answer:

Null hypothesis: $\mu_{2002}\leq 3.15$

Alternative hypothesis :$\mu_{2002} > 3.15$  

C. The mean Rutgers College GPA has increased to more than 3.15

Step-by-step explanation:

Data given and notation  

$\bar X_{2000}=3.15$ represent the average score for Rutgers College in 2000

$\bar X_{2002}=3.46$ represent the average score for Rutgers College in 2002

$s_{2000}$ represent the sample standard deviation  in 2000

$s_{2002}$ represent the sample standard deviation  in 2002

$n$ sample size  

State the null and alternative hypotheses.  .  

What are H0 and Ha for this study?  

Null hypothesis:  $\mu_{2002}\leq 3.15$

Alternative hypothesis :$\mu_{2002} > 3.15$  

For this case we need to take in count that the alternative hypothesis can't have and = sign, and based on the information a good hypothesis here would be if the average GPA increased between 2000 and 2002, so based on this the best option for this case would be:

C. The mean Rutgers College GPA has increased to more than 3.15