Can Dogs Detect Malaria? A study was conducted to determine wh...

Question

Can Dogs Detect Malaria? A study was conducted to determine whether dogs could detect malaria from socks worn by malaria patients and socks worn by patients without malaria. Among 175 socks worn by malaria patients, the dogs made correct identifications 123 times. Among 145 socks worn by patients without malaria, the dogs made correct identifications 131 times (based on data presented at an annual meeting of the American Society of Tropical Medicine, by principal investigator Steve Lindsay). Use a 0.05 significance level to test the claim of no difference between the two rates of correct responses.

c. What do the results suggest about the use of dogs to detect malaria?

c. What do the results suggest about the use of dogs to detect malaria?

Accepted Answer

All right. Hello, everyone. So this question says, a researcher wants to know if a new training method affects the accuracy of dogs in detecting a specific scent. In a test, 160 trials were conducted with dogs using the new method. And the dogs correctly identified the scent in 110 cases. In another group using the standard method, 130 trials were conducted, and the dogs correctly identified the scent in 104 cases. At the 0.05 significance level test the claim that Using a hypothesis test, that there is no difference in the rates of correct identification between the two methods. What do the results imply about the test's effectiveness? OK, so first, let's define the hypothesis. The null hypothesis or H knot. would state that piece of 1 is equal to piece of 2, or that P1 is equal to P2. So, for this problem, let's say that P1 is a proportion of correct identifications for the new method, and P2 is a proportion for the standard method. The alternative hypothesis on the other hand. Which state that there is a difference in proportions, meaning that P1 is not equal to P2. So now let's calculate the sample proportions. Or pea hat for both cases. Now, the sample proportion is equal to the correct number of identifications divided by the total number of trials. So for Phat 1, that would be 110 divided by 160. Which gives you 0.6875. He had 2 For the standard method is equal to 104 correct identifications divided by 130, which equals 0.8. So now, to proceed with calculating the standard error, we have to find the pooled proportion, or just Phat. So the pooled proportion is used when assuming that the null hypothesis is that the proportions are equal. So in this case, Phat is equal to the number of correct identifications in both trials, divided by. The total number of trials across both methods. So that's 110. Added to 104. Divided by 160 added to 130. And so this gives you approximately 0.7379. Which you can then use to calculate the standard error. So let's do that. The standard error if you recall. Is equal to the square root of Phat. Multiplied by one subtracted by Phat. And multiplied by 1 divided by N1, added to 1 divided by N2. So now substituting the values that we have, the standard error. is equal to 0.7379. Multiplied by 1 subtracted by 0.7379. Multiplied by one. Divided by 160, added to 1 divided by 130. So now this gives you a standard error of approximately 0.0519. Which we can now use to compute the test statistic, or Z in this case. So now Z Is equal to he had one. Subtracted by Piha 2. Divided by the standard error. So that's 0.6875, subtracted by 0.8. And divided by 0.0519. And so this gives you a Z score of approximately -2.17 after rounding. At this point The next step is to find the critical value and compare. Right, so in this context, we're using a two-tailed test at the 0.05 significance level. Which means that the critical Z value. is equal to approximately positive and negative 1.96. This means that the rejection region is outside of -1.96 and 1.96. So, our test value of -2.17 is less than -1.96, which means that it is outside of the rejection range, or excuse me, it's in the rejection range, considering it's outside of both numbers. So Because our test value falls within the rejection region, we can reject the null hypothesis. And so now this leads us to our final answer, which reads as follows. Z is equal to -2.17, rejects the null hypothesis. There is sufficient evidence at the 0.05 significance level to conclude that there is a significant difference in the rates of correct identification between the two methods. This conclusion implies that the new training method might not be as effective as the standard method for teaching dogs to detect a specific scent. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

Key Concepts

Hypothesis Testing

Significance Level

P-Value

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