60% of those who get a specific type of cancer are released healthy after 2 year

Question

60% of those who get a specific type of cancer are released healthy after 2 years. In an observation of 127 patients they saw that 79 of them were released healthy after 2 years. Is it possible to say with a 99% confidence that 60% of patients are released healthy after 2 years?

Make a hypothesis test.

(Your answer has to include: What distribution you use (z, t or chi square), what is the H0 and H1, what is the significance level of alfa 0,01. What is the critical value of the distribution you are using. Calculated value, the p value and results in the end (whether you reject the H0 or not and on what grounds)

Explanation / Answer

We use the Z distribution for this n>30 ,we have a large sample size.

Ho: p0 = .60

Ha: p0!= .60

p = x.n = 78/127 = .622

So, first find the Z test statistic:

Z = (p-p0)/sqrt(p0*p0'/n) = (.622-.60)/sqrt(.60*.40/127) = .51, p-value is 1-.6915 = .3085

The critical value at 99% Confidence is Z = 2.575, The critical Z value is 2.575 which is more than .51.

The, p-value is .3085 , and it much greater than alpha = .01 , we don't reject null hypothesis.

Hence,

Ha: p0= .60

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