Question

This question relates to Question 2. Suppose the environmentalist wanted to check if the air quality had improved in recent years. A more comprehensive study was thus conducted in 2018. This time the concentration of NO2 was measured hourly at thirty randomly selected monitoring stations. The data are stored in q5.csv. (a) Using Welch’s two-sample t test, determine if the NO2 levels have significantly lowered. Test using the 5% level of significance. [6 marks] [Hint: you will need to combine the two datasets in a particular format in order to perform the test using R Commander. Check Section 7.2 of the Study Guide.] (b) State the statistical assumptions underlying the Welch’s two-sample t test. Demonstrate if the assumptions are valid or not for these data. [3 marks] (c) Is it appropriate to use the paired t test to conduct the test here? Explain your answer. [2 marks]

( Question 2 was The dataset below contains the concentration of NO2 measured hourly measured at twenty randomly selected monitoring stations across Australia in 2013. According to the National Air Quality Standards1 , it is a concern if the NO2 concentration exceeds 0.12 ppm. An environmentalist wished to know if there is a concern or not. (a) Based on the information provided, write down the null and alternative hypotheses that the environmentalist would like to test. [1 mark] (b) Write down the name of the test you are going to use. [1 mark] (c) Write down the decision rule. [1 mark] (d) Paste the output from R Commander. (If you would like to do it by hand, calculate the test statistic and show the steps.) [1 mark] (e) Do you reject the null hypothesis or not? Explain your answer. [1 mark] (f) Draw a conclusion which answers the original problem. [1 mark] (g) State and check all the assumptions for the hypothesis test you have used. [3 marks]

dataset: Question 2

NO2_2013
0.108
0.122
0.165
0.194
0.116
0.084
0.095
0.141
0.15
0.146
0.126
0.126
0.132
0.068
0.101
0.061
0.304
0.116
0.052
0.165

Data for question 5:

NO2_2018
0.095
0.099
0.099
0.083
0.092
0.087
0.098
0.096
0.098
0.104
0.093
0.082
0.079
0.098
0.097
0.082
0.07
0.09
0.089
0.096
0.097
0.094
0.089
0.076
0.078
0.097
0.096
0.076
0.059
0.112

Answer 1

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