Scenario #4: Bottle Caps Topic: One sample t-interval & test for a population mean A machine makes twist-off caps for bottles. The machine is adjusted to make caps of diameter 1.85 cm. production records show that when the machine is so adju so adjusted it will make caps with mean diameter 1.85 cm. During production, an inspector checks the diameters of caps to see if the machine has slipped out of adjustment. A random sample of 50 caps has a mean diameter of 1.87 cm with a standard deviation of 0.05 cm. YOU MAY ASSUME ALL APPROPRIATE CONDITIONS HAVE BEEN MET. a) Give a 95% confidence interval for the true mean diameter of caps being produced by this machine. b) Is there significant evidence at the 5% level that the mean from this sample is greater than the true value of 1.85 cm? (Again, assume appropriate conditions have been met.) M = 1 185 * = 1.87 2 = (1. 87 - 1 85 ) 1 (,05 / 569 ) = 3.2 5 = .OS P- val = 00 14 10014- ,05 50 we resect the null hypothesis, there is significant evidence at the 5 % level that the mean from this sample is greater c) Do your results from parts a and b agree? Explain your