Question

Use the information below to answer the CANCER SURVIVAL questions that follow. Data originally from DASL http://lib.stat.cmu.edu/DASL/Datafiles/CancerSurvival.html e. Some bronchial cancer patients had the following survival times (in days) after receiving a certain treatment: 20, 37, 63, 64, 72, 81, 138, 151, 155, 166, 166, 223, 245, 246, 450, 459. (The second instance of "166" is not a mistake.) Do these numbers suggest that the average survival time, for all bronchial cancer patients who receive that treatment, is significantly different from 200 days?

Answer 1

Let X denote the survival time of bronchial cancer patients.

Let denote the sample mean of given sample.

X

$\bar X=\frac{\sum X_i}{n}=171$

S denote the sample standard deviation.

$S=\frac{\sum (X_i-\bar X)^2}{n-1}=131.19$

To check if the average survival time, for all bronchial cancer patients is significantly different from 200 days.

Ho : = 200
versus $H_1:\mu\neq 200$

That is, the alternative hypothesis is, The average survival time is not equal to 200 days.

Test statistic: $T=\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}$

Under H₀ the test statistic follows t-distribution with n-1=16-1=15 degrees of freedom.

T = -0.8561

P-value = P[ |t₁₅| > 0.8561 ] = 0.4054

At 10% level of significance, p-value > 0.10

Hence, we do not reject H₀.

That is the average survival time is 200 days.

As you had not mentioned which 3 steps you wanted, I performed whole test. Hope you find the solution helpful.