Exposure to Volatile Organic Compounds (VOCs), which have been identified in indoor air, is suspecte

Question

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 $26.0$. 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] 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$^{2}$. 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] 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]

Accepted Answer

Reject $H_0$; 1.45%; significance level is smaller

2019 VJC P2 Q9

2019 VJC P2 Q9

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