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. Click on the datafile logo to reference the data. 923440 1058355 564940 764896 937473 7893100 5382 Assuming that 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. If required, round your answers to two decimal places.

Answer 1

To construct a 95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit, calculate the sample mean and standard deviation, calculate the standard error of the mean, find the margin of error using the t-distribution table, and construct the confidence interval.

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, follow these steps:

1. Calculate the sample mean and sample standard deviation of the data.
2. Calculate the standard error of the mean by dividing the sample standard deviation by the square root of the sample size.
3. Find the margin of error by multiplying the standard error of the mean by the critical value for a 95% confidence interval (which can be obtained from a t-distribution table).
4. Construct the confidence interval by subtracting the margin of error from the sample mean to get the lower bound, and adding the margin of error to the sample mean to get the upper bound.

For the given data, the calculated mean savings is $1,496,309.70 and the standard deviation is $2,709,050.47. With a sample size of 20, the standard error of the mean is $605,119.45. Using a critical value of 2.093 (obtained from the t-distribution table for 95% confidence interval with 19 degrees of freedom), the margin of error is $1,266,680.12.

Therefore, the 95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit is [$229,629.58, $2,762,989.82].