Question

Health insurers are beginning to offer telemedicine services online that replace the common office visit. Wellpoint provides a video service that allows subscribers to connect with a physician online and receive prescribed treatments. Wellpoint claims that users of its LiveHealth Online service saved a significant amount of money on a typical visit. The data shown below ($), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by Wellpoint.
90 34 41106 84 5355 48 4175 49 9792 73 7480 94 10256 83

Required:
Assuming the population is roughly symmetric, construct a 95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit (to 2 decimals).

Answer 1

Answer:

$71.35-2.093\frac{22.48}{\sqrt{20}}=60.83$    

$71.35+2.093\frac{22.48}{\sqrt{20}}=81.87$    

Step-by-step explanation:

Information given

90 34 41 106 84 53 55 48 41 75 49 97 92 73 74 80 94 102 56 83

In order to calculate the mean and the sample deviation we can use the following formulas:  

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)  

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)  

$\bar X=71.35$ represent the sample mean for the sample  

$\mu$ population mean (variable of interest)

s=22.48 represent the sample standard deviation

n=20 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$   (1)

The degrees of freedom are given by:

$df=n-1=20-1=19$

Since the Confidence is 0.95 or 95%, the significance is $\alpha=0.05$ and $\alpha/2 =0.025$, and the critical value would be $t_{\alpha/2}=2.093$

And replacing we got:

$71.35-2.093\frac{22.48}{\sqrt{20}}=60.83$    

$71.35+2.093\frac{22.48}{\sqrt{20}}=81.87$