The owner of cake house said that the shelf life of its product Chococake is normally distributed with mean 140 hours and standard deviation 40 hours. In an effort to increase the shelf life, the cake house spent a large amount of money on a new packaging technique.
a. Using a random sample of 100 newly-packed Chococake, it is found that the mean shelf life is 154 hours. Can the cake house manager conclude that the new packaging technique is efficient at 0.01 significance level?
b. Based on the result in a), what type of error could possibly occur? Explain the effect of this error to the cake house.
c. Another random sample of 150 newly-packed Chococake is analyzed and it is found that 127 of the Chococake expired after 140 hours. Can we conclude from this new study that more than 80% of the Chococake expired after 140 hours? Use 0.01 siginificance level.