The HEPA filter manufacturer claims that their product reduces CO2 levels by more than 300 ppm. Both the sign test and the Wilcoxon signed-rank test are appropriate for testing this claim, but the t-test is not.
The sign test is suitable because it is a non-parametric test that does not rely on any assumptions about the distribution of the data. It compares the number of positive and negative differences between the observed and expected values. In this case, the expected value would be a reduction of more than 300 ppm. By comparing the number of positive differences to the number of negative differences, we can determine if the claim is statistically significant.
The Wilcoxon signed-rank test is also appropriate because it is a non-parametric test that compares the ranks of the observed differences. It does not assume a normal distribution and can be used when the data is not normally distributed. This test is useful when the data is measured on an ordinal scale or when the assumptions of the t-test are not met.
On the other hand, the t-test is not suitable for testing this claim because it assumes that the data is normally distributed. Additionally, the t-test requires the data to be measured on a continuous scale, which may not be the case for CO2 levels. Therefore, the t-test should not be used in this scenario.