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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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