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	34	40
104	84	54
55	50	40
75	46	95
92	75	75
80	94	100
56	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

Confidence interval for the population when population standard deviation is not known:

Given:

x :  sample of 20 online doctor visits, are consistent with the savings per visit reported by Wellpoint

	x: Savings per visit	(x-)	(x-)2
	91	19.85	394.0225
	104	32.85	1079.1225
	55	-16.15	260.8225
	75	3.85	14.8225
	92	20.85	434.7225
	80	8.85	78.3225
	56	-15.15	229.5225
	34	-37.15	1380.1225
	84	12.85	165.1225
	50	-21.15	447.3225
	46	-25.15	632.5225
	75	3.85	14.8225
	94	22.85	522.1225
	83	11.85	140.4225
	40	-31.15	970.3225
	54	-17.15	294.1225
	40	-31.15	970.3225
	95	23.85	568.8225
	75	3.85	14.8225
	100	28.85	832.3225
Total	1423		9444.55
Mean:	71.15

sample size : n= 20

Sample mean of savings for a televisit to the doctor :

Sample standard deviation of savings for a televisit to the doctor :

Given
Sample Mean :	71.15
Sample Standard Deviation : s	22.2953
Sample Size : n	20
Degrees of freedom : n-1	19
Confidence Level :	95
	0.05
/2	0.025
	2.093

95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit

95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit = (60.72, 81.58)

95% confidence interval: $60.72 to $81.58 per visit