Question

1. The following data is the survival time of a set of patients who had Glioblastoma (it is the time from detection until death): {5.28, 6.36, 9.72, 0.25, 5.52, 0.24, 76.8, 15.12, 11.52, 21.84, 2.76, 5.4, 15, 4.8, 1.08}.

• Determine a 90% confidence interval for the median of the data and a 90% confidence interval for the mean of the data.

Answer 1

Following is the ordered data set:

S.No.	X
1	0.24
2	0.25
3	1.08
4	2.76
5	4.8
6	5.28
7	5.4
8	5.52
9	6.36
10	9.72
11	11.52
12	15
13	15.12
14	21.84
15	76.8

Sample size is n=15

Since we need to confidence interval for median so quantile q will be q=0.5

Since nq =7.5 and n(1-q) = 7.5 both are greater than 5 so we can use large sample method. That is we can find confidence interval using binomial distribution.

The critical value of z for 90% confidence interval is 1.645.

Using binomial distribution we have

Therefore

That is 90% confidence interval for median is from 5th observation to 11th observation. Since 5th observation of ordered data set from table is 4.8 and 11th observation is 11.52 so required confidence interval is (4.8, 11.52).

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Following table shows the mean and SD of data:

	X	(X-mean)^2
	0.24	140.968129
	0.25	140.730769
	1.08	121.727089
	2.76	87.478609
	4.8	53.479969
	5.28	46.689889
	5.4	45.064369
	5.52	43.467649
	6.36	33.097009
	9.72	5.726449
	11.52	0.351649
	15	8.334769
	15.12	9.042049
	21.84	94.614529
	76.8	4184.407969
Total	181.69	5015.180895

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