1. A bearing used in an automotive application is supposed to have a nominal inside diameter of 1.5 inches. A random sample of 20 bearings is selected and the data on the inside diameter is as follows:
1.48 1.50 1.51 1.495 1.487 1.505 1.48 1.52 1.50 1.515 1.50
1.49 1.49 1.509 1.489 1.49 1.512 1.51 1.495 1.50
Bearing diameter is known to be approximately normally distributed with a standard deviation of 0.01 in. Test the hypothesis that the mean inside diameter has changed. Use a 0.01 significance level.
2. A producer of chocolate bars hypothesizes that his production does not adhere to the weight standard of 100g. As a measure of quality control, he weighs a random sample of 15 bars and obtains the following results in grams:
96.40, 97.64, 98.48, 97.67, 100.11, 95.29, 99.80, 98.80, 100.53, 99.41, 97.64, 101.11, 93.43, 96.99, 97.92.
It is assumed that the production process is standardized in the sense that the variation is controlled to be σ = 2. Is there sufficient evidence to support the producer’s hypothesis? Perform a test at the 5% significance level.