Question

Experience has shown that the greater the impact resistance the quality of steel is better. The characteristics of the steel before applying the heat treatment indicate that the average and standard deviation of the population are 20 tons and 9 tons respectively. A random sample of 36 steel specimens is extracted after the heat treatment is applied and the results indicate that the mean and the standard deviation of the sample are: 23 ton and 6.5 ton. It is suspected that heat treatment produces increase in impact resistance. It shows if the data that was obtained from a experiment confirm that suspicion.

a) Establish the hypothesis and make a diagram indicating the acceptance region and the region of

b) Calculate the critical value using a level of significance of 5%, and calculate the statistic observed.

c) Establish decision and conclusion.

d) Find the p-value. Interpret this result.

e) Calculate the probability of committing the type II error, assuming that after applying the treatment the average was 25 tons. Finally, indicate if the experiment has value.

Answer 1

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