Question

In an effort to improve scores on college-entrance exams, the principal at a large high school chooses 35 students
at random who have already taken the exam. The students are enrolled in a six-week prep course to improve their
scores. After the prep course, the students take the college-entrance exam again. The mean difference (first-
second) in exam scores is -1.75 points with a standard deviation of 7.12 points. Assuming the conditions for
inference are met, what is the test statistic for testing the hypotheses Hoi Hoi = 0; He Moip <0?
O 1-1.75 -0
7.12
35
o
0+ 1.75
7.12
35
-1.75 -0
7.12
35
=
1.75 -0
7.12
35
Nex
Submit
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Answer 1

Using the t-distribution, it is found that the test statistic for the hypotheses test is given by:

$t = \frac{-1.75 - 0}{\frac{7.12}{\sqrt{35}}}$

What are the hypotheses tested?

At the null hypotheses, it i tested if the mean difference remains the same, that is:

$H_0: \mu  = 0$

At the alternative hypotheses, it is tested if it has decreased, hence:

$H_a: \mu < 0$.

What is the test statistic?

The test statistic is given by:

$t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$

The parameters are:

• $\overline{x}$ is the sample mean.

• $\mu$ is the value tested at the null hypothesis.

• s is the standard deviation of the sample.

• n is the sample size.

The parameters are given as follows:

$\overline{x} = -1.75, s = 7.12, n = 35$.

Hence the test statistic is given by:

$t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{-1.75 - 0}{\frac{7.12}{\sqrt{35}}}$

More can be learned about the t-distribution at https://brainly.com/question/16162795

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