1.A cereal box filling machine is designed to release an amount of 16 ounces of cereal into each box, and the machine's manufacturer wants to know of any departure from this setting. The engineers at the factory randomly sample 150 boxes of cereal and find a sample mean of 15.75 ounces. If we know from previous research that the population is normally distributed with a standard deviation of 1.46 ounces, is there evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance? State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.

2.A manufacturer of widgets wants to test a new widget-producing machine to determine if it can make an average of 25 widgets per second before deciding to invest in the machine. The standard to reject the new machine is if it makes an average of less than 25 widgets per second. Here are data from a small random sample:

25.6, 26.2, 22.5, 20.5, 26.4, 27.4, 23.6, 26.9, 25.7, 24.9

Assuming the population follows a normal distribution, is there evidence that the new machine should be rejected at the 0.01 significance level?State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.

3.In manufacturing processes, it is of interest to know with confidence the proportion of defective parts. Suppose that we want to be reasonably certain that less than 4% of a company's widgets are defective. To test this, we obtain a random sample of 250 widgets from a large batch. Each of the 250 widgets is tested for defects, and 6 are determined to be defective, based upon the manufacturer's standards. Using = 0.01, is this evidence that less than 4% of the company's widgets are defective?State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.

4.In 1965, about 44% of the U.S. adult population had never smoked cigarettes. A national health survey of 1360 U.S. adults (selected randomly) during 2020 revealed that 626 had never smoked cigarettes. Using = 0.05, test whether there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes. State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.