2019 VJC P2 Q9

Exposure to Volatile Organic Compounds (VOCs), which have been identified in indoor air, is suspected as a cause of headaches and respiratory systems.Indoor plants have not only a positive psychological effect on humans, but may also improve the air quality.Certain species of indoor plants were found to be effective removers of VOCs.

A commonly known VOC is Benzene. The following data gives the benzene levels, \(x\)(in ppm) in \(40\) test chambers containing the indoor plant Epipremnum aureum.

\(n=40\), \(\sum{\left( x-26.0 \right)=-30.1}\), \({{\sum{\left( x-26.0 \right)}}^{2}}=214.61\).

The initial mean Benzene level (in ppm) without Epipremnum aureum was found to be \(26.0\).

1. Test, at the \(5\)% level of significance, the claim that the mean Benzene level, \(\mu \)(in ppm), has decreased as a result of the indoor plant Epipremnum aureum. You should state your hypotheses clearly.[5]
2. State, giving a reason, whether there is a need to make any assumptions about the population distribution of the Benzene level in order for the test to be valid.[2]

The Benzene levels of another \(50\) test chambers containing the indoor plant Epipremnum aureum were recorded. The sample mean is \(\bar{x}\)ppm and the sample variance is \(8.33\) ppm\(^{2}\).

3. The acceptance region of a test of the null hypothesis \(\mu =26.0\) is \(\bar{x}>25.1\). State the alternative hypothesis and find the level of significance of the test.[4]
4. If the null hypothesis is \(\mu ={{\mu }_{0}}\), where \({{\mu }_{0}}>26.0\), would the significance level of a test with the same acceptance region in part (iii) be larger or smaller than that found in (iii)? Give a reason for your answer.[2]