The elasticity of plastic can vary depending on the process by which the plastic

Question

The elasticity of plastic can vary depending on the process by which the plastic is prepared. To compute the elasticity of plastic produced by two different processes, 5 samples from each process were analyzed for elasticity. The data are shown below. Process A: 6.1, 8.2, 7.7, 8.6, 7.1. Process B: 9.1, 9.2, 8.6, 8.9, 7.9 At alpha = 0.05 level of significance, test if the mean elasticity of Process A is less than the mean elasticity of Process B. Test the claim at 0.05 level of significance. Test statistic t = mu_1 - mu_2/squareroot s^2_1/n_1 + s^2_2/n_1 State the null and alternative hypothesis. State your conclusion for your hypothesis test.

Explanation / Answer

Q.2

(A) Null Hypothesis : H0 : Mean elasticity of process A is equal to process B.

Alternative Hypothesis : Ha : Mean elasticity of process A is less than process B.

Mean of population A A = 7.54 ; variance s12 = 0.963

Mean of population B B = 8.74 ; variance s22 = 0.273

so Test Statistic :

t = (A - B ) / sqrt [ s12 /n1 + s22 /n2 ] =  ( 7.54 - 8.74)/ sqrt [ 0.963/5 + 0.273/5] = -1.2/ 0.4972 = -2.4135

for alpha = 0.05 and

dF =  [ s12 /n1 + s22 /n2 ]2 / [(s12 /n1)2 / (n1 -1) + (s22 /n2)2 /(n2 -1)] = 6.099 = 6

so Criitcal value of tcrit = 1.943

so Here ltl > tcrit so we can reject the null hypothesis and can say that mean of process A is higher than Mean of process B.

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