A simple random sample of 12 students took a class designed to improve their SAT scores. Following are their scores before and after the class. Before 972 988 992 998 998 998 1000 1050 1050 1050 1080...

A simple random sample of 12 students took a class designed to improve their SAT scores. Following are their scores before and after the class.

Can you conclude that the mean increase in score is less than 15 points?

If we let:

Let μ
₁be the population mean SAT scores before the coaching class, and μ
₂be the population mean SAT scores after the coaching class.

Let μ
_dbe the population mean difference of SAT scores after and before the coaching class, i.e. μ
₂- μ₁

Round to three decimal places if necessary.

a) Use "mu1" for μ
₁ , "mu2" for μ₂,and "mu.d" for μ
_d.

   Null hypothesis H₀
:

    Alternate hypothesis H₁
:

b) Type of test:  left or right or two

c) significance level: α =

d) Test statistic:

Clear state whether test statistic in this claim is z or t. For example, "z=1.2345"

e) Compute p-value of the test statistic.

f)  Decision:  . Type "yes" if reject null hypothesis. Type "no" if not to reject null hypothesis.