Question

The data below are the survival times after treatment (in days) of some advanced colon cancer patients who were treated with ascorbate.

248, 377, 189, 1843, 180, 537, 519, 455, 406, 365, 942, 776, 372, 163, 101, 20, 283

(a)

i) What is the point estimate for the average or mean of this data?

ii) Report an appropriate 96% confidence interval estimate for the mean survival time after treatment of all advanced colon cancer patients who might be treated with ascorbate. Assume the survival times are normally distributed and take Standard Deviation to be 427.17.

iii) Interpret the confidence interval in words and in context.

(b) Based on the data at hand, would 600 days be considered a reasonable guess as to the average survival time?

(c) What was the margin of error (ME) of the confidence interval?

(d) If we wanted to be 99% confident that our estimate was within 60 days of the population mean survival time, how many patients should we observe?

(e) If the sample included more patients, would the 96% confidence interval have been narrower or wider?

Answer 1

(a)

(i)

The point estimate for the average or mean of this data = = 7776/17 = 457.41

(ii)

n = 17

s = 427.17

SE = s/

= 427.17/

= 103.61

= 0.04

ndf = 17 - 1 = 16

From Table, critical values of t = 2.2354

Confidence interval:

457.41 (2.2354 X 103.61)

= 457.41 231.60

= ( 225.81 ,689.01)

Confidence Interval:

225.81 <    <   689.01

(iii)

The 96% Confidence Interval 225.81 <    <   689.01 is a range of values we are 96% confidence contains the population mean survival time after treatment of all advanced colon cancer patients who might be treated with ascorbate.

(b)

Since 600 is included in the Confidence Interval, 600 days would be considered a reasonable guess as to the average survival time.

(c)

Margin of Error = ME = 2.2354 X 103.61 = 231.60

(d)

Number of patients (n) is given by:

Given:

= 0.01

From Table, critical values of Z = 2.576

= 427.17

e = 60

Substituting, we get:

So,

Answer is:

337

(e)

If the sample included more patients, the 96% confidence interval would have been narrower.