Answer:
![\text {CI} = (60.54, \: 81.46)\\\\](https://tex.z-dn.net/?f=%5Ctext%20%7BCI%7D%20%3D%20%2860.54%2C%20%5C%3A%2081.46%29%5C%5C%5C%5C)
Therefore, we are 95% confident that actual mean savings for a televisit to the doctor is within the interval of ($60.54 to $81.46)
Step-by-step explanation:
Let us find out the mean savings for a televisit to the doctor from the given data.
Using Excel,
=AVERAGE(number1, number2,....)
The mean is found to be
Let us find out the standard deviation of savings for a televisit to the doctor from the given data.
Using Excel,
=STDEV(number1, number2,....)
The standard deviation is found to be
![s = \$ 22.35](https://tex.z-dn.net/?f=s%20%3D%20%5C%24%2022.35)
The confidence interval is given by
![\text {confidence interval} = \bar{x} \pm MoE\\\\](https://tex.z-dn.net/?f=%5Ctext%20%7Bconfidence%20interval%7D%20%3D%20%5Cbar%7Bx%7D%20%5Cpm%20MoE%5C%5C%5C%5C)
Where the margin of error is given by
![$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\](https://tex.z-dn.net/?f=%24%20MoE%20%3D%20t_%7B%5Calpha%2F2%7D%28%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%20%7D%20%29%20%24%20%5C%5C%5C%5C)
Where n is the sample of 20 online doctor visits, s is the sample standard deviation and
is the t-score corresponding to a 95% confidence level.
The t-score is given by is
Significance level = α = 1 - 0.95 = 0.05/2 = 0.025
Degree of freedom = n - 1 = 20 - 1 = 19
From the t-table at α = 0.025 and DoF = 19
t-score = 2.093
So, the margin of error is
![MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 2.093\cdot \frac{22.35}{\sqrt{20} } \\\\MoE = 2.093\cdot 4.997\\\\MoE = 10.46\\\\](https://tex.z-dn.net/?f=MoE%20%3D%20t_%7B%5Calpha%2F2%7D%28%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%20%7D%20%29%20%5C%5C%5C%5CMoE%20%3D%202.093%5Ccdot%20%5Cfrac%7B22.35%7D%7B%5Csqrt%7B20%7D%20%7D%20%5C%5C%5C%5CMoE%20%3D%202.093%5Ccdot%204.997%5C%5C%5C%5CMoE%20%3D%2010.46%5C%5C%5C%5C)
So the required 95% confidence interval is
![\text {CI} = \bar{x} \pm MoE\\\\\text {CI} = 71 \pm 10.46\\\\\text {CI} = 71 - 10.46, \: 71 + 10.46\\\\\text {CI} = (60.54, \: 81.46)\\\\](https://tex.z-dn.net/?f=%5Ctext%20%7BCI%7D%20%3D%20%5Cbar%7Bx%7D%20%5Cpm%20MoE%5C%5C%5C%5C%5Ctext%20%7BCI%7D%20%3D%2071%20%5Cpm%2010.46%5C%5C%5C%5C%5Ctext%20%7BCI%7D%20%3D%2071%20-%2010.46%2C%20%5C%3A%2071%20%2B%2010.46%5C%5C%5C%5C%5Ctext%20%7BCI%7D%20%3D%20%2860.54%2C%20%5C%3A%2081.46%29%5C%5C%5C%5C)
Therefore, we are 95% confident that actual mean savings for a televisit to the doctor is within the interval of ($60.54 to $81.46)