1. A textile mill weaves cloth that is used to make sheets. The top grade of sheets has at least 200 threads per inch. (Because higher thread count indicates higher quality, it will not matter if the thread count is above 200.) Random samples from 20 areas of a piece of cloth result in an average thread count of y = 190 with s = 50. Assuming normality, test the appropriate hypothesis using a = 0.05, and explain what your results mean.
2. A toothpaste was formulated with a silica content of 3% by weight. The manufacturer randomly samples 33 tubes of toothpaste and finds their mean silica content is 3.4% and the standard deviation is 0.43%. Test the hypothesis that the mean silica content is not on target using a p-value and a = 0.05. Explain what the results of your test indicate in terms the manufacturer can understand.