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.

92	34	41
104	84	55
55	48	38
75	50	94
92	72	74
77	91	101
52	82

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

Solution :

Given data 92,104,55,75,92,77,52,34,84,48,50,72,91,82,41,55,38,94,74,101

=> sum of terms = 92 + 104 + 55 + 75 + 92 + 77 + 52 + 34 + 84 + 48 + 50 + 72 + 91 + 82 + 41 + 55 + 38 + 94 + 74 + 101 = 1411

=> Number of terms n = 20

=> Mean x = Sum of terms/Number of terms

= 1411/20

= 70.55

=> Standard deviation s = 22.18

=> df = n - 1 = 19

=> For 95% confidence interval , t = 2.093

=> The 95% confidence interval for the mean is

=> x +/- t*s/sqrt(n)

=> 70.55 +/- 2.093*22.18/sqrt(20)

=> 60.17 to 80.93