See below.

Question

An experiment tests whether or not dogs can detect cancer by sniffing 7 urine vials, one of which was from a cancer patient. When the hypothesis is tested that the dogs randomly guess, H0: p = 1/7, against the hypothesis that the dogs do not randomly guess, Ha: p not equal 1/7, a P-value of 0.05 is obtained. If the decision in part a is in error, what type of error is it? Explain using the context of the experiment. A - A Type I Error - The P value would cause the rejection of the hypothesis that the dogs randomly guess when in reality they have a method for determining the cancer vial. B- A Type II error - The P value would cause the rejection of the hypothesis that the dogs randomly guess when in reality they do randomly guess. C - A Type I error - The P value would cause the rejection of the hypothesis that the dogs randomly guess when in reality they do randomly guess. D. A Type II error - The P value would not cause rejection of the hypothesis that the dogs randomly guess when in reality they have a method for determining the cancer vial.

Answer 1

I'm not sure this question is well-worded. What is meant by "if the decision in part a is in error"? No decision or inference is mentioned, so we can't be sure of the question's intent.

 

However, the topic being questioned is clear, i.e. the difference between a Type I and Type II error. A Type I is the rejection of the null hypothesis when it was actually true, i.e. "declaring" a difference which in fact does not exist. A Type II error is the failure to reject the null hypothesis when it was false, i.e. "missing" a real difference. Being gullible means making more Type I errors, and being skeptical means making more Type II errors. 

 

Now back to the ambiguous question. It might mean to say "since the p value was 0.05 the null hypothesis was rejected; if that rejection was in error then what type of error was it, I or II?" Untangling that means that there is no real difference and the null hypothesis is true but was rejected by the investigator who incorrectly concluded that there was a difference. Which type of error is that?

 

However, the p value being 0.05 does not automatically imply that the investigator would reject the null hypothesis, hence the question is unclear.