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.

91	33	41
106	84	57
56	50	37
76	50	97
92	74	73
79	92	100
53	83

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).

95% confidence interval: $_______ to $________ per visit

Answer 1

Sample Size ,    n =     20
Sample Mean,      x̅ = ΣX/n =     71.2000

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   22.4373

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   19          
't value='   tα/2=   2.093   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   22.4373/√20=   5.0171          
margin of error , E=t*SE =   2.0930   *   5.0171   =   10.501
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    71.20   -   10.5010   =   60.6990
Interval Upper Limit = x̅ + E =    71.20   -   10.5010   =   81.7010

95%   confidence interval is (   60.70   < µ <   81.70   )

................

thanks

please upvote