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Sagot :
From the information given, we have that:
1. The null hypothesis is: [tex]H_0: \mu = 85[/tex]
2. The t-statistic is t = 3.78.
Item 1:
We want to test if there is a significant difference from the population mean of 85, thus, at the null hypothesis, it is tested if the population mean is of 85, that is:
[tex]H_0: \mu = 85[/tex]
Item 2:
The t-statistic is given by:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which:
- X is the sample mean.
- [tex]\mu[/tex] is the value tested at the null hypothesis.
- s is the sample standard deviation.
- n is the sample size.
For this problem, we have that: [tex]X = 90, \mu = 85, s = 7, n = 28[/tex]. Then:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{90 - 85}{\frac{7}{\sqrt{28}}}[/tex]
[tex]t = 3.78[/tex]
The t-statistic is t = 3.78.
A similar problem is given at https://brainly.com/question/25193176
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