A melting point test of n=10 samples of a binder usedin manufacturing a rocket p

Question

A melting point test of n=10 samples of a binder usedin manufacturing a rocket propellant resulted in xbar=154.2 degrees F. Assume that the melting point is normally distrubted with standard deviation = 1.5 degrees F.

a) Check the assumptions necessary to test Ho: = 155 vs. Ha: # 155 at the 1% significance level. [If you don't know if an assumption is satisfied based on the information provided, then state "We must assume b) Calculate the test statistic. c) Find the p-value. d) Make a decision. e) State the conclusion in terms of the problem. f) Construct a confidence interval (CI) to test the hypotheses. Make a decision based on the Cl. Does your decision match the decision in (d)? g) Describe a type l error in terms of the problem. h) What is the consequence of making a type l error? Suppose the binder would not be used if there's enough evidence for Ha. 155 because it would be deemed unsafe. i Describe a type Il error in terms of the problem. j) What is the consequence of making a type Il error? Suppose the binder would be used if there's not enough evidence for HaJL 155 because it is thought to be safe. k) Which error could have been made here? l) What is the probability of making a type Il error, if the true mean is 153°F? m) What is the power of the test, if the true mean is 153°F? n) Suppose now that the true mean is 150°F. Without doing the calculation, would the power of the test be lrge or smaller than the answer in the previous part?

Explanation / Answer

(a) Null Hypothesis (Ho): µ = 155

Alternative Hypothesis (Ha): µ 155

(b) Test Statistics Z = (X-bar - µ)/ (/n)

Z = (154.2 – 155)/ (1.5/10)

Z = -1.69

(c) P-value = 2*P (Z < -1.69) = 2*0.045514 = 0.0910

(d) Level of significance, = 0.01

Using Z-tables, the critical value is Z(0.01/2) = Z(0.005) = ± 2.576

Since -1.69 < -2.576, we fail to reject the null hypothesis.

(e) we conclude that there is not sufficient evidence to support the claim that that the melting point is not equal to 155 oF.

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