Question: Refer to the sample results that are listed below, for the measured nicotine contents of randomly selected filtered and non-filtered king size cigarettes. Use a significance level of 0.05, to test the claim that king size filters have a lower mean amount of nicotine that the mean amount of nicotine in non filtered king size cigarettes.

Filtered Kings Non-Filtered Kings

n₁ = 21 n₂ = 8

\({{\bar{X}}_{1}}=0.94\) \({{X}_{2}}=1.65\)

s₁ = 0.31 s₂ = 0.36

(a) State the null and alternative hypothesis

(b) Find the t-statistics

(c) Find the critical value

(d) Construct a 90% confidence interval for the difference between two means

(e) Do cigarette filters appear to be effective at reducing nicotine?