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.
4,364 5,595 2,724 4,936 4,475
4,789 6,453 4,122 4,245 3,804
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).
Mean is 4550.7 (add up the numbers and divide by 10)
I'll let you determine standard deviation. Use a calculator, or if you do it by hand, use a formula to calculate the standard deviation.
2.5 that is the deviation
a. To find the point estimate of the mean cost per treatment with Herceptin, we need to calculate the sample mean. The formula for the sample mean is:
Sample Mean = (Sum of all observations) / (Number of observations)
Calculating the sample mean:
Sum of all observations = 4,364 + 5,595 + 2,724 + 4,936 + 4,475 + 4,789 + 6,453 + 4,122 + 4,245 + 3,804 = 45,497
Number of observations = 10
Sample Mean = 45,497 / 10 = 4,549.7
Therefore, the point estimate of the mean cost per treatment with Herceptin is $4,549.7.
b. To find the point estimate of the standard deviation of the cost per treatment with Herceptin, we need to calculate the sample standard deviation. The formula for the sample standard deviation is:
Sample Standard Deviation = sqrt[(Sum of squared differences from the mean) / (Number of observations - 1)]
Calculating the sample standard deviation:
Step 1: Calculate the mean (already calculated in part a) = $4,549.7
Step 2: Calculate the squared differences from the mean for each observation and sum them up:
(4,364 - 4,549.7)^2 = 194,986.92
(5,595 - 4,549.7)^2 = 1,090,540.1
(2,724 - 4,549.7)^2 = 3,845,981.29
(4,936 - 4,549.7)^2 = 150,146.92
(4,475 - 4,549.7)^2 = 5,543.61
(4,789 - 4,549.7)^2 = 57,303.29
(6,453 - 4,549.7)^2 = 3,655,967.61
(4,122 - 4,549.7)^2 = 182,443.61
(4,245 - 4,549.7)^2 = 92,384.41
(3,804 - 4,549.7)^2 = 429,012.49
Sum of squared differences from the mean = 9,092,318.15
Step 3: Calculate the sample standard deviation using the formula mentioned earlier:
Sample Standard Deviation = sqrt[(9,092,318.15) / (10 - 1)] = sqrt(1,014,702.0167) ≈ 1007.3
Therefore, the point estimate of the standard deviation of the cost per treatment with Herceptin is approximately 1007.3 dollars (to 1 decimal).
To develop a point estimate of the mean cost per treatment with Herceptin, you need to calculate the sample mean.
a. Point Estimate of the Mean:
To calculate the sample mean, you sum up all the costs and divide by the number of patients:
Sample Mean = (4,364 + 5,595 + 2,724 + 4,936 + 4,475 + 4,789 + 6,453 + 4,122 + 4,245 + 3,804) / 10
= 45,497 / 10
= 4,549.7
So, the point estimate of the mean cost per treatment with Herceptin is $4,549.7.
b. Point Estimate of the Standard Deviation:
To calculate the point estimate of the standard deviation, you need to use the sample data.
First, calculate the sample variance by following these steps:
1. Subtract the sample mean from each treatment cost and square the result.
(4,364 - 4,549.7)^2 = 313,148.09
(5,595 - 4,549.7)^2 = 1,088,232.49
(2,724 - 4,549.7)^2 = 3,312,480.09
(4,936 - 4,549.7)^2 = 150,194.49
(4,475 - 4,549.7)^2 = 5,580.09
(4,789 - 4,549.7)^2 = 57,144.49
(6,453 - 4,549.7)^2 = 3,638,730.49
(4,122 - 4,549.7)^2 = 183,578.89
(4,245 - 4,549.7)^2 = 93,061.29
(3,804 - 4,549.7)^2 = 551,931.84
2. Sum up all the squared differences.
313,148.09 + 1,088,232.49 + 3,312,480.09 + 150,194.49 + 5,580.09 + 57,144.49 + 3,638,730.49 + 183,578.89 + 93,061.29 + 551,931.84 = 5,395,082.65
3. Divide the sum of squared differences by (n-1), where n is the number of patients in the sample (10 in this case).
Sample Variance = 5,395,082.65 / (10 - 1) = 599,453.63
Finally, take the square root of the sample variance to get the point estimate of the standard deviation:
Point Estimate of Standard Deviation = √599,453.63 ≈ 774.4 (rounded to 1 decimal)
So, the point estimate of the standard deviation of the cost per treatment with Herceptin is approximately 774.4 dollars.