An industrial chemist is investigating the concentration of a stabilizing agent in two different formulations of a polymer, Type A and Type B. Random samples of 80 specimens from Type A and 100 specimens from Type B are tested, and the concentration, ccc parts per million (ppm), is measured for each.
The following table summarizes the experimental results:
FormulationSample size (n)∑c∑c2Unbiased estimate of meanUnbiased estimate of varianceType A80416021647852.02.0Type B1005250276120mv\begin{array}{|l|c|c|c|c|c|} \hline \text{Formulation} & \text{Sample size } (n) & \sum c & \sum c^2 & \text{Unbiased estimate of mean} & \text{Unbiased estimate of variance} \\ \hline \text{Type A} & 80 & 4160 & 216478 & 52.0 & 2.0 \\ \hline \text{Type B} & 100 & 5250 & 276120 & m & v \\ \hline \end{array}FormulationType AType BSample size (n)80100∑c41605250∑c2216478276120Unbiased estimate of mean52.0mUnbiased estimate of variance2.0vDetermine the value of mmm and the value of vvv.
The chemist suspects that the mean concentration in Type A is significantly lower than the mean concentration in Type B.
Test the chemist's suspicion at the 1% level of significance. State your hypotheses and critical value clearly.
Explain the importance of the Central Limit Theorem in the context of this hypothesis test.