Question

Begin this discussion by first stating your intended future career. Then give an example of a mean that applies to two Populations for which you would like to do a Hypothesis Test in your future career. In your Hypothesis Test you will be testing the difference between these two Population means when the two samples are independent. Your discussion MUST include the two target Populations along with the Population characteristic that your mean is computed for, and the unit that is used when taking the sample measurements. As shown in the text your Null and Alternative Hypotheses MUST include a symbol for each of the two Population means along with the relational operator that describes the difference being tested between these two parameters as stated in your discussion.

Answer 1

Example -

A guidance counselor claims that high school students in a college preparation program have higher ACT scores than those in a general program. The sample mean ACT score for 49 high school students who are in a college preparation program is 22.2 and the sample standard deviation is 4.8. The sample mean ACT score for 44 high school students who are in a general program is 20.0 and the sample standard deviation is 5.4.  

Use an 8% level of significance to conduct test the guidance counselor’s claim. Assume the distribution of ACT scores for both programs are approximately normally distributed. Assume that σ_{college prep}² ‡ σ_general²

Let denotes the mean ACT score for high school students who are in a college preparation program and denotes the mean ACT score for high school students who are in a general program.

Level of significance (α):   α = 0.08

Type of test : right tail

Conclusion : There is sufficient evidence to support the guidance counselor’s claim that high school students in a college preparation program have higher ACT scores than those in a general program.