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 Live Health Online service saved a significant amount of money on a typical visit. The data shown below (s), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by Wellpoint. Click on the datafile logo to reference the data. DATA file 105 56 76 93 78 83 49 48 74 93 82 55 40 95 73 100 Assuming that 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. If required, round your answers to two decimal places. $ 60.54 to $ 81.46 Icon Rey

Answer 1

Answer:

I 95%(μ)= [64.26; 85.74]

Step-by-step explanation:

The confidence interval formula is:  

I (1-alpha) (μ)= mean+- [(t(n-1))* S/sqrt(n)]  

alpha= is the proportion of the distribution tails that are outside the confidence interval. In this case, 5% because 100-95%  

t(n-1)= is the critical value of the t distribution with 16-1 degrees of freedom for an area of alpha/2 (2.5%). In this case is 2.1314

We use the t-student distribution because the population standard deviation is unknown.

S= sample standard deviation. In this case 20.152

mean= 75

n= number of observations =16

The DATA file shows have 16 observations

Then, the confidence interval (95%):  

I 95%(μ)= 75+- [2.1314*(20.152/sqrt(16))]  

I 95%(μ)= 75+- [10.7379]  

I 95%(μ)= [75-10.7379; 75-10.7379]  

I 95%(μ)= [64.2620; 85.7379]  

I 95%(μ)= [64.26; 85.74]