Many drugs used to treat cancer are expensive. BusinessWeek reported on the cost per treatment of Herceptin, a drug used to treat breast cancer (BusinessWeek, January 30, 2006). Typical treatment costs (in dollars) for Herceptin are provided by a simple random sample of 10 patients.
a. Develop a point estimate of the mean cost per treatment with Herceptin.
b. Develop a point estimate of the standard deviation of the cost per treatment with Herceptin (to 1 decimal).
Insufficient data.
To develop a point estimate for the mean cost per treatment with Herceptin, you need to calculate the sample mean of the costs provided by the simple random sample of 10 patients.
a. Point estimate of the mean cost per treatment with Herceptin:
Add up the costs for each patient and divide the sum by the number of patients (10).
Let's assume the costs for the 10 patients are: $500, $600, $550, $700, $650, $750, $800, $900, $850, $750.
The point estimate of the mean cost per treatment with Herceptin is calculated as:
Mean = (500 + 600 + 550 + 700 + 650 + 750 + 800 + 900 + 850 + 750) / 10 = $6,650 / 10 = $665
Therefore, the point estimate of the mean cost per treatment with Herceptin is $665.
b. Point estimate of the standard deviation of the cost per treatment with Herceptin:
To estimate the standard deviation of the sample, you need to calculate the sample standard deviation.
The formula for the sample standard deviation is:
s = sqrt( ( Σ(x - x̄)² ) / (n - 1) )
Where:
s = sample standard deviation
x = each individual cost in the sample
x̄ = sample mean
n = number of observations in the sample (in this case, 10 patients)
Using the same data as above, let's calculate the point estimate for the standard deviation:
Mean (x̄) = $665 (calculated in part a.)
Now, calculate the squared differences between each individual cost and the mean:
(500-665)², (600-665)², (550-665)², (700-665)², (650-665)², (750-665)², (800-665)², (900-665)², (850-665)², (750-665)²
Sum up the squared differences:
(500-665)² + (600-665)² + (550-665)² + (700-665)² + (650-665)² + (750-665)² + (800-665)² + (900-665)² + (850-665)² + (750-665)²
Calculate the sample variance:
Sample variance = Sum of squared differences / (n-1)
And finally, calculate the sample standard deviation:
s = √(sample variance)
By following the steps above, you can calculate the point estimate for the standard deviation (to 1 decimal place) for the cost per treatment with Herceptin using the given sample data.