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.

a. Test the claim using a hypothesis test.

a. Test the claim using a hypothesis test.

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 using a hypothesis test that there is no difference in the rates of correct identification between the two methods. All right, so here we can distinguish between the null and the alternative hypotheses. The null hypothesis or H not. would state that there are no differences in the proportions of correct identifications between the two methods. So for example, If we say that P1. Is the proportion of identifications with the new method and P2 is the proportion for the standard method. The null hypothesis states that P1 is equal to P2. But the alternative hypothesis simply states that there is a difference between the two, which means that P1 would not be equal to P2. So now let's find the sample portions. Starting off with the new methods thou be P1. P1 in this case would be equal to. The 110 correct identifications divided by the 160 trials. So that gives you 0.6875. P2, on the other hand, for the standard method. Would be 104 correct identifications divided by 130. And that equals 0.8. So now we also have to consider the pool proportion. And the pull proportion is used when you assume that the no. Hypothesis Is correct, which means that the proportions are equal. So the pulled proportion or Phat is equal to. The sum of correct identifications for both methods, divided by the total number of trials for both methods. So here that's. The sum of 110 and 104. Added to the sum of 160. And 130. And this equals approximately 0.7379. So from here, with the pools proportion, you would calculate the standard error of the difference between the two proportions. So recall that standard error. Is equal to. He had Multiplied by one subtracted by Phat. And multiplied by 1 divided by N1. Added to 1 divided by N2. Now keep in mind that N1 and N2 correspond to the number of trials for the new method and standard method respectively. So substituting that information. Gives you SE equal to 0.7379. Multiplied by 1 subtracted by 0.7379. And then multiplied by. 1 divided by 160. Added to 1 divided by 130. And so this gives you a standard error of approximately 0.0519. Which now leads you into the test statistic or Z. So here, the Z score. is going to use the difference in proportions. So that's P1 subtracted by P2 divided by the standard error that was just obtained. So Z Is equal to 0.6875 Subtracted by 0.8. And then divided by 0.0519. And this gives you approximately 2.17. So with our test statistic, we now have to determine the critical value and compare, right? So with a two-tailed test, At alpha equals 0.05. The critical Z value. Is approximately positive or negative 1.96. And so because of that, the rejection region is outside of -1.96 and 1.96. So now let's go back to our calculated value. In this case, -2.17 is less than -1.96, which means that it falls in the rejection. In the rejection region. Which means therefore, that we can reject the null hypothesis. So this leads us now to the final answer, which I went ahead and pre-wrote on the screen here. First, Z is equal to -2.17, which means we reject 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. And 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

Chi-Square Test

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