Question

Exercise 1: Thirty nine women with a diagnosis of inoperable or metastatic breast cancer have been followed-up for a number of years, while under continuous treatment with a medication called trastzuzumab. The time (in months) each patient remained in remission was recorded. Remission is is a decrease or disappearance of signs and symptoms of cancer. Below is the data. 50 74 35 39 21 37 27 35 30 35 26 38 34 34 26 41 61 33 33 26 25 41 35 34 44 33 60 61 42 30 80 31 24 49 26 31 28 41 37. 1. Are there any outliers in the sample? If so, indicate their values. 2. Compute the 45-th percentile of the remission time. 3. Find a 97% confidence interval for the average remission time

Answer 1

Exercise 1:

1) We can make a boxplot using R to detect outliers.

The boxplot is given below.

From the boxplot, we can see that 4 values are outside the range. Those four values are the outliers here.

So the 4 outlier points are:

60, 61(2 times), 74, 80.

2)

Using R, the value of 45 th percentile of the data is 34.

3)

So a 97% confidence interval for average remission time is (33.3043, 42.9521).

The R code is attached.

x=c(50,74,35,39,21,37,27,35,30,35,26,38,34,34,26,41,61,33,33,26,25,41,35,34,44,33,60,61,42,30,80,31,24,49,26,31,28,41,
37)
boxplot(x, main="BOXPLOT", ylab="Time(in months)")
quantile(x,0.45)