Question

Please do as little intermediate rounding as possible in order to get the correct p-value.

In a sample of 200 of Deadpool's severed arms, 110 of them grow back a new Deadpool. In a sample of 210 of Deadpool's legs, 90 of them grow back a new Deadpool.  

(a) Do we have evidence at the various levels that Deadpool's severed arms are more likely to grow back a new Deadpool than his severed legs?
The associated p-value for this hypothesis test is ( )? (Answers to four places after the decimal.)

(b)Do we have evidence at the various levels that Deadpool's severed arms and his severed legs have a different probability of growing back a new Deadpool?
The associated p-value for this hypothesis test is ( )?

Answer 1

p1 = Proportion of arms growing back = 110 / 200 = 0.55

p2 = Proportion of legs growing back = 90 / 210 = 0.4286

p = pooled proportion = (110 + 90) / (200 + 210) = 200 / 410 = 0.4878

1 - p = 0.5128

The Test Statistic

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(a) The Hypothesis:

H0: p1 = p2

Ha: p1 > p2

This is a right tailed test

The p value (Right Tail) = 0.0069

Therefore at the levels of = 0.01, 0.05, 0.1, we would reject the null hypothesis.

Yes it is more likely that Deadpools severed arms will grow back than his legs

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(b) The Hypothesis:

H0: p1 = p2

Ha: p1 p2

This is a right tailed test

The p value (Two Tail) = 0.0138

At = 0.01 we would fail to reject the null hypothesis. There wouldn't be enough evidence to conclude that there is a difference in probability of growing back Deadpools arms and legs.

At = 0.05, 0.10 we would reject the null hypothesis. There would be enough evidence to conclude that there is a difference in probability of growing back Deadpools arms and legs

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