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.

90 33 41
105 83 56
56 48 41
76 47 96
94 74 74
80 91 98
54 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

Using the given data, we find that the 95% confidence interval for the mean savings is $60.82 to $78.48 per visit.

Step-by-step explanation:

To construct a 95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit, we can use the formula:

CI = X-bar ± (t-value) * (s/√n)

Where X-bar is the sample mean, t-value is the critical value from the t-distribution table, s is the sample standard deviation, and n is the sample size.

Using the given data, we find that the mean savings (X-bar) is $69.65, the sample standard deviation (s) is $20.67, and the sample size (n) is 20. The t-value for a 95% confidence interval with 19 degrees of freedom is approximately 2.093.

Plugging these values into the formula, we get:

CI = $69.65 ± (2.093) * ($20.67/√20)

CI = $69.65 ± $8.83

Therefore, the 95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit is $60.82 to $78.48 per visit.