Answer:
The test statistic is t = 3.36.
Step-by-step explanation:
You're testing the claim that the mean difference is greater than 0.7.
At the null hypothesis, we test if the mean difference is of 0.7 or less, that is:
![H_0: \mu \leq 0.7](https://tex.z-dn.net/?f=H_0%3A%20%5Cmu%20%5Cleq%200.7)
At the alternate hypothesis, we test if the mean difference is greater than 0.7, that is:
![H_1: \mu > 0.7](https://tex.z-dn.net/?f=H_1%3A%20%5Cmu%20%3E%200.7)
The test statistic is:
![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 standard deviation of the sample and n is the size of the sample.
0.7 is tested at the null hypothesis:
This means that ![\mu = 0.7](https://tex.z-dn.net/?f=%5Cmu%20%3D%200.7)
A survey of 35 people was conducted to compare their self-reported height to their actual height.
This means that ![n = 35](https://tex.z-dn.net/?f=n%20%3D%2035)
From the sample, the mean difference was 0.95, with a standard deviation of 0.44.
This means that ![X = 0.95, s = 0.44](https://tex.z-dn.net/?f=X%20%3D%200.95%2C%20s%20%3D%200.44)
Calculate the test statistic
![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{0.95 - 0.7}{\frac{0.44}{\sqrt{35}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B0.95%20-%200.7%7D%7B%5Cfrac%7B0.44%7D%7B%5Csqrt%7B35%7D%7D%7D)
![t = 3.36](https://tex.z-dn.net/?f=t%20%3D%203.36)
The test statistic is t = 3.36.