A chemist developing insect repellents wishes to know if a newly developed formula gives greater protection from insect bites than that given by the leading product on the market. In the experiment, 14 volunteers each had one arm spayed with the old product and the other sprayed with the new formula. Then each subject placed his arms into two chambers filled with equal number of mosquitoes, gnats and other biting insects. The numbers of bites received on each arm are as follows:

To test the new formula is more effective than the old one:

(i) State null and alternative hypotheses

(ii) Can you apply both parametric and non-parametric tests in this problem and why?

(iii)Write the assumptions to apply the suitable parametric test.

(iv)Apply the parametric test by assuming the assumptions write in part (iii) are fulfilled and write the conclusion.

(v) Apply the non-parametric test and write the conclusion.

(vi)Compare the conclusions drawn in parts (iv) and (v)

(i) State null and alternative hypotheses:

Null Hypothesis (H0): The new formula for insect repellent is equally effective as the old formula.
Alternative Hypothesis (Ha): The new formula for insect repellent is more effective than the old formula.

In statistical terms:
H0: μ_old = μ_new
Ha: μ_old > μ_new

Where:
- μ_old represents the population mean number of insect bites with the old formula.
- μ_new represents the population mean number of insect bites with the new formula.

(ii) Can you apply both parametric and non-parametric tests in this problem and why?

Yes, you can apply both parametric and non-parametric tests in this problem, depending on the assumptions and characteristics of the data.

Parametric tests are appropriate when certain assumptions about the data are met, including:
1. Normality: The data should follow a normal distribution.
2. Independence: Observations should be independent of each other.
3. Homogeneity of variances: Variances in both groups should be roughly equal.

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