From the information given, we have that:
1. The null hypothesis is: ![H_0: \mu = 85](https://tex.z-dn.net/?f=H_0%3A%20%5Cmu%20%3D%2085)
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 <u>tested if the population mean is of 85</u>, that is:
![H_0: \mu = 85](https://tex.z-dn.net/?f=H_0%3A%20%5Cmu%20%3D%2085)
Item 2:
The t-statistic is given by:
![t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%7D)
In which:
- X is the sample mean.
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:
. Then:
![t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![t = \frac{90 - 85}{\frac{7}{\sqrt{28}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B90%20-%2085%7D%7B%5Cfrac%7B7%7D%7B%5Csqrt%7B28%7D%7D%7D)
![t = 3.78](https://tex.z-dn.net/?f=t%20%3D%203.78)
The t-statistic is t = 3.78.
A similar problem is given at brainly.com/question/25193176