Final answer:
Hypothesis testing for whether the mean maintenance time for machine 1 is less than machine 2 involves formulating H0 and Ha, calculating a test statistic, and comparing the p-value to α. For preventive maintenance times and work weeks, probabilities are calculated using statistical functions or distributions such as normalcdf and uniform distribution probabilities.
Step-by-step explanation:
To address the student's question regarding the hypothesis that the mean maintenance time for machine 1 is less than that for machine 2, one would typically conduct a hypothesis test for the difference between two means. The hypothesis testing process involves several steps:
- Formulating a null hypothesis (H0) and an alternative hypothesis (Ha).
- Using a test statistic and the provided sample data to calculate the statistic's value.
- Determining the p-value and comparing it to the level of significance (α), often set to 0.05, to make a decision on whether to reject or fail to reject the null hypothesis.
For the prevention maintenance of air conditioners, using normalcdf (E - 99,1.1,1,-V70) = 0.7986 suggests an 80 percent chance the service time will be less than 1.1 hours. However, considering a 20 percent risk of exceeding the allotted time, it might be wise to schedule more time.
When testing whether the mean work week for engineers is less than 60 hours based on a sample, it involves calculating the sample mean and standard deviation and conducting a t-test, given the small sample size (t-test).
In example 5.6, to find probabilities involving uniformly distributed data, such as the time a furnace repair requires, one would calculate areas under the uniform distribution curve (uniform distribution probabilities).