6 A pollution control officer is investigating a possible link between the levels of various pollutants in the air and the speed of the wind at various sites. A random sample of 60 values of the windspeed together with the levels of a variety of pollutants is taken at a particular site. The product moment correlation coefficient between wind-speed and nitrogen dioxide level is 0.3231 .

1. Carry out a hypothesis test at the \(10 \%\) significance level to investigate whether there is any correlation between wind-speed and nitrogen dioxide level.
2. State the condition required for the test carried out in part (a) to be valid. Table 6.1 shows the values of the product moment correlation coefficient between 5 different measures of pollution and also wind-speed for a very large random sample of values at another site. Those correlations that are significant at the \(10 \%\) level are denoted by a * after the value of the correlation. \begin{table}[h]

   Correlations	PM10	SPEED	\(\mathrm { NO } _ { 2 }\)	\(\mathrm { O } _ { 3 }\)	PM25	\(\mathrm { SO } _ { 2 }\)
   PM10	1.00
   SPEED	0.08*	1.00
   \(\mathrm { NO } _ { 2 }\)	0.59*	0.25*	1.00
   \(\mathbf { O } _ { \mathbf { 3 } }\)	-0.05*	-0.04*	-0.30*	1.00
   PM25	0.85*	-0.01	0.56*	-0.02	1.00
   \(\mathrm { SO } _ { 2 }\)	0.42*	0.15*	0.73*	-0.63*	0.40*	1.00

   \captionsetup{labelformat=empty} \caption{Table 6.1}
   \end{table} \begin{table}[h]
   \captionsetup{labelformat=empty} \caption{Table 6.2 shows standard guidelines for effect sizes.}

   Product moment correlation coefficient	Effect size
   0.1	Small
   0.3	Medium
   0.5	Large

   \end{table} Table 6.2 The officer analyses these data for effect size.
3. Explain how the very large sample size relates to the interpretation of the correlation coefficients shown in Table 6.1.
4. Comment briefly on what the pollution control officer might conclude from these tables, relevant to her investigation into wind-speed and pollutant levels.