Measuring and controlling variation is important for quality control purposes in both the manufacturing and the service sector. A manufacturer of metal bolts took a sample of 50 bolts and found that the standard deviation of their lengths was 1.3 mm. Assume that the length of bolts follows a normal distribution.

1. Engineering specifications actually require that the standard deviation should be exactly 1 mm. Test at the 5% level of significance whether these specifications are met given the sample data.

2. Would your conclusion change if the significance level had been 1% instead of 5%? Why, why not?