Question

Dogs can be trained to detect diseases in humans by sniffing certain human secretions. In 54 trials, a sniffer dog was presented with 7 vials of secretions (6 from healthy individuals, 1 from a person with a disease). In 14 out of the 54 trials, the sniffer dog correctly identified the vial from the person with the disease. The test is judged to be useless if the dogs are essentially guessing, but there is some hope for improvement if the dogs react in some way that suggests that they are not guessing.

10) [6 marks] The population consists of all possible trials of this kind that this dog could be submitted to. What would be the parameter and random variable associated with each trial?

11) [6 marks] State the hypotheses for the trial that could be used to see if there was evidence that the dog was not guessing.

12) [10 marks] If the null hypothesis is true, then find the p-value for this test. You will need to use one of the following probabilities to do this: P[6 or more correct identifications] = 0.802 P[6 or fewer correct identifications] = 0.332 P[14 or more correct identifications] = 0.0173 P[14 or fewer correct identifications] = 0.9827

13) [5 marks] At a level of 0.1, is there evidence that the null hypothesis should be rejected? Explain, briefly. [Note: if you were unable to get a value from the previous question, assume that the p-value was 0.145].

14) [25 marks] State the meaning of the value 0.1 used as a significance level in this test, in the context of this question. I have a midterm monday, SOS

Answer 1

10)

Parameter is true proportion of trials in which the dog correctly identified the vial from the person with the disease.

Random variable is sample proportion of trials in which the dog correctly identified the vial from the person with the disease.

11)

If the dog was not guessing, the probability of correctly guessing is more than 1/7. Note, a random guess would have 1/7 probability of correctly guessing.

Null hypothesis H0: p = 1/7

Alternative hypothesis Ha: p > 1/7

12)

Sample number of trials with correctly guess = 14

If the null hypothesis is true, the  probability of correctly guessing a random trial is 1/7.

p-value is the probability of correctly guessing more than 14 trials out of 54 where the probability of correctly guessing a random trial is 1/7.

P[14 or more correct identifications] = 0.0173

12)

Since, p-value is less than 0.1 significance level, we reject null hypothesis H0 and conclude that there is strong evidence that

p > 1/7 and thus the dogs was not guessing.

14)

The value 0.1 is the Type I error. It means the probability of rejecting a correct null hypothesis. That is, the probability to reject the null hypothesis that the dogs was guessing (p = 1/7) is 0.1 where in reality the dogs was guessing.