Hello ! I would like to check if my answers are correct for this problem and understand the question I couldn't answer.
Thank you very much for your help

For 57 cities, air quality was compared for NO2 and SO2 levels which were then classified in low or high quantity.

22 cities had low NO2 and SO2
15 cities had high NO2 and SO2
9 cities had high SO2 and low NO2
11 cities had high NO2 and low SO2

1) What proportion of towns have a high SO2 level ? Give a 95% confidence intervall of this proportion.
2) Is the probability of observing a high NO2 level significantly different (at 5%) depending on whether SO2 levels are high or low.
3) Are high levels of NO2 and SO2 significantly different (at 5%) ?



1) 24/57 villes have high SO2. I don't see how to get the confidence intervall.

2)

. SO2+ SO2-
NO2+ 15 11 26
NO2- 9 22 31
24 33 57


Expected values table :
. SO2+ SO2-
NO2+ 11 15 26
NO2- 13 18 31
24 33 57


S = (15-11)/11 + (11-15)/15 + (9-13)/13 + (22-18)/18 = 4,64

The test follow a Chi-square law uder H0. At 5%, the value of the table is 3,841. We do not reject H0, there is no link between the two variables.


3) S = (b-c) / (b+c) = (11-9) / 20 = 0,2

The test follow a Chi-square law under H0. We do not reject H0, the value of SO2 and are not significantly different under a 5% error assumption.