i need answer

4. [15 marks] The World Health Organization (WHO) monitors air quality in some cities around the world. The primary measure is concentration of certain particles suspended in air (given in rag/m3]. An Australian researcher wants to compare air quality for the city centres of Melbourne and Houston, Texas (a US city of similar size). This study is of interest to the WHO because Melbourne has taken many initiatives to encourage commuters to use environmentally friendly forms of transportation such as walking or cycling while Houston has not. A random sample of measurements from each city were collected and they are summarised below: Air Quality (pg/m ) mean standard deviation sample size Melbourne 72.9 25.6 13 Houston 81.7 28.3 16 i) Use a hypothesis test to nd out if there is evidence that the average number of suspended particles is greater in Houston than in Melbourne. In your answer: a] State clearly the hypotheses H0 and H1. 0" J State the test statistic and its distribution assuming Hg is true. c] Calculate the observed value of the test statistic. d Give an expression for the P-value and then calculate this value. You can use the following RStudio output values to help you calcu- late the above P-uulue; pt(0.869, 27) = 0.8037 pt(0.869_. 28) = 0.8039 pt(0.869, 29) = 0.3040 Pt(-0.369, 27) = 0.1963 pt(-0.869, 23) = 0.1961 pt(-0.B69, 29) = 0.1960 pt(1.869, 27) = 0.9637 pt(1.869, 28) = 0.9639 pt(1.869, 29) = 0.9641 pt(-1.869, 27) = 0.0363 pt(-1.869, 23) = 0.0361 pt(-1.B69, 29) = 0.0359 e] State your conclusion in simple language. ii) What assumptions are required for the hypothesis test in Part i) to be valid? Clearly state these assumptions. Please see over . . . iii) A researcher wants to assess any benets Wall: to Work Day may have on Melbourne's air quality. Air quality measurements will be taken the week before and the week after next year's Walk to Work Day (3rd Sep 2021). What would be an appropriate test here? Give a reason for your choice