Problem:
A company claims that its new Calamansi Hand Soap kills 99% of bacteria. To test this claim, a researcher conducts an experiment on 30 randomly selected samples and finds that the soap kills an average of 97% of bacteria, with a standard deviation of 3%.
Using a significance level of α=0.05\alpha = 0.05α=0.05, test the company’s claim that the soap kills 99% of bacteria.
Instructions:
- State the null hypothesis and the alternative hypothesis.
- Perform a one-sample z-test (assume the sample size is large enough for normal approximation).
- Compute the z-statistic.
- Determine the critical value or p-value and decide whether to reject or fail to reject the null hypothesis.
