Question: Data for suspended particulate matter in air particles at two sites are given below in \[\mu gms/{{m}^{3}}\].

Site 1: 68 22 36 32 42 24 28 38 35 37

Site 2: 36 38 39 40 36 35 34 33 32 37

Complete the table below:

(a) Calculate the standard error of the mean difference without assuming equal variances.

(b) Create back to back stem plots for the data.

(c) Calculate a 95% confidence interval for \[{{\mu }_{1}}-{{\mu }_{2}}\], again without assuming equal variance. Use the conservative degrees of freedom to help calculate the confidence interval.

(d) State the null and alternative hypothesis and determine the two-sided p-value for testing: \[{{H}_{0}}:{{\mu }_{1}}={{\mu }_{2}}\].

(e) Compare you results against a significant level of 0.05 and interpret your results.