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	35	39
107	84	55
56	48	38
76	49	94
92	72	74
76	92	99
55	81

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

Population is symmetric ,here population standard deviation is unknown so we will follow t distribution

X	X-Mean	(X-Mean)²
91	20.35	414.1225
107	36.35	1321.3225
56	-14.65	214.6225
76	5.35	28.6225
92	21.35	455.8225
76	5.35	28.6225
55	-15.65	244.9225
35	-35.65	1270.9225
84	13.35	178.2225
48	-22.65	513.0225
49	-21.65	468.7225
72	1.35	1.8225
92	21.35	455.8225
81	10.35	107.1225
39	-31.65	1001.7225
55	-15.65	244.9225
38	-32.65	1066.0225
94	23.35	545.2225
74	3.35	11.2225
99	28.35	803.7225
Mean=70.65		∑(X-Mean)²=9376.55

Mean(x̅)=70.65

Standard Deviation(s)=sqrt(∑(X-Mean)²/(n-1))=sqrt(9376.55/19)=22.215

n=20

Degree of freedom=n-1=19

critical value at 95% confidence wih 19 degree of freedom (t)=2.093 (using t table)

95% confidence interval is given by:

x̅ ± t*(s)/sqrt(n)

=70.65±2.093*22.215/sqrt(20)

=70.65±10.40

=(60.25, 81.05)