Question

3) Experience has shown that the greater the resistance to impact the quality the quality of the 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 the heat treatment produces an increase in impact resistance. Show your data that was obtained from an experiment confirm this suspicion a) Establish the hypothesis and make a diagram indicating the acceptance region and the rejection region. b) Calculate the critical value using a level of significance of 5% and calculate the observed statistic. c) Establish your decision and conclusion. d) Find the p-value. Interpret this result. e) Calculate the probability of committing the type Il error, assuming that after applying the treatment the average was 25 tons. Finally, indicate if the experiment has value.

Answer 1

Given -hed we Can cli o Alternate hypotheses H1:以フ20 23 -> Yejec-ion ares Ce CCepten egion ReSec P/Z 1-G 4s) ㆁ.os. る 6 V36

Resect Ho, d) P-valse, 2 . 0228