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HELP ASAP, PLEASE!!!!
A school is implementing an SAT preparation program. To study the program's effectiveness, the school looks at participants' SAT scores before starting the program and after completing the program. The results are shown in the table:
A B C D E F G
Before 1060 980 1140 1040 1000 960 1200
After 1040 1020 1180 1040 980 1020 1240
Difference 20 -40 -40 0 20 -60 -40

How is the test statistic calculated. (Note that intermediate calculations have been rounded to 2 decimal places.)

HELP ASAP PLEASE A School Is Implementing An SAT Preparation Program To Study The Programs Effectiveness The School Looks At Participants SAT Scores Before Star class=

Sagot :

Using the t-distribution, as we have the standard deviation for the sample, we have that the test statistic is given by:

[tex]t = \frac{-20 - 0}{\sqrt{\frac{32.66}{7}}}[/tex]

What are the hypothesis tested?

At the null hypothesis, it is tested if there is no difference, that is:

[tex]H_0: \mu = 0[/tex]

At the alternative hypothesis, it is tested if there is a difference, that is:

[tex]H_1: \mu \neq 0[/tex]

What is the test statistic?

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

  • [tex]\overline{x}[/tex] is the sample mean.
  • [tex]\mu[/tex] is the value tested at the null hypothesis.
  • s is the standard deviation of the sample.
  • n is the sample size.

In this problem, [tex]\mu = 0[/tex] is tested at the null hypothesis, and the sample is: 20, -40, -40, 0, 20, - 60, -40, hence:

[tex]\overline{x} = -20, s = \sqrt{32.66}, n = 7[/tex].

Hence, the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{-20 - 0}{\frac{\sqrt{32.66}}{\sqrt{7}}}[/tex]

[tex]t = \frac{-20 - 0}{\sqrt{\frac{32.66}{7}}}[/tex]

More can be learned about the t-distribution at https://brainly.com/question/16313918

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