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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.