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.

Verified step by step guidance

1. Step 1: Define the null and alternative hypotheses. The null hypothesis (H₀) states that there is no difference between the two rates of correct responses (p₁ = p₂). The alternative hypothesis (H₁) states that there is a difference between the two rates of correct responses (p₁ ≠ p₂).
2. Step 2: Calculate the sample proportions for each group. For socks worn by malaria patients, the sample proportion is p₁ = 123 / 175. For socks worn by patients without malaria, the sample proportion is p₂ = 131 / 145.
3. Step 3: Compute the pooled proportion (p̂) using the formula: p̂ = (x₁ + x₂) / (n₁ + n₂), where x₁ and x₂ are the number of correct identifications for each group, and n₁ and n₂ are the total number of socks in each group.
4. Step 4: Calculate the standard error (SE) for the difference in proportions using the formula: SE = √[p̂(1 - p̂)(1/n₁ + 1/n₂)].
5. Step 5: Compute the test statistic (z) using the formula: z = (p₁ - p₂) / SE. Then, compare the test statistic to the critical value for a two-tailed test at a significance level of 0.05, or use the p-value approach to determine whether to reject or fail to reject the null hypothesis.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) that represents no effect or difference, and an alternative hypothesis (H1) that indicates the presence of an effect or difference. The goal is to determine whether the observed data provide sufficient evidence to reject the null hypothesis at a specified significance level, often denoted as alpha (α).

Significance Level

The significance level, commonly set at 0.05, is the threshold for determining whether the results of a hypothesis test are statistically significant. It represents the probability of rejecting the null hypothesis when it is actually true (Type I error). If the p-value obtained from the test is less than the significance level, the null hypothesis is rejected, suggesting that there is a statistically significant difference between the groups being compared.

Chi-Square Test

The Chi-Square test is a statistical method used to determine if there is a significant association between categorical variables. In this context, it can be applied to compare the rates of correct identifications by dogs for socks worn by malaria patients versus those worn by non-malaria patients. The test calculates the expected frequencies under the null hypothesis and compares them to the observed frequencies to assess whether any differences are statistically significant.