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. 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).

a) $27.37 to $72.63 per visit
b) $41.16 to $58.84 per visit
c) $30.21 to $69.79 per visit
d) $37.29 to $62.71 per visit

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 the margin of error. The 95% confidence interval is $1,132.78 to $5,527.22 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 need to calculate the sample mean and the margin of error.

1. Calculate the sample mean: Add up all the savings values and divide by the sample size. In this case, the sample mean is ($1,200 + $2,200 + $3,000 + $3,600 + $4,000 + $4,200 + $4,200 + $4,000) / 20 = $3,330.
2. Calculate the standard deviation of the sample: Subtract the sample mean from each savings value, square the differences, add them all up, divide by the sample size minus 1, and take the square root of the result. In this case, the standard deviation is approximately $1,051.14.
3. Calculate the margin of error: Multiply the standard deviation by the appropriate t-value from the t-distribution table for a 95% confidence level and the given sample size (in this case, 20). The t-value for a 95% confidence level and 20 degrees of freedom is approximately 2.093. Multiply this by the standard deviation to get the margin of error, which is approximately $2,197.22.
4. Construct the confidence interval: Subtract the margin of error from the sample mean to get the lower bound, and add the margin of error to the sample mean to get the upper bound. In this case, the 95% confidence interval is $3,330 - $2,197.22 to $3,330 + $2,197.22, which simplifies to $1,132.78 to $5,527.22. Rounded to 2 decimal places, the confidence interval is $1,132.78 to $5,527.22 per visit.