1. A company sells packets of cheese crackers that they claim on average, contain at least 20g of cheese crackers. They admit that their claim is wrong (and will refund any money), if a sample of 40 cheese crackers have a mean less than 19.8g. If the standard deviation is 0.5g, determine the critical value that specifies the rejection region.
2. A researcher wishes to test the claim of a particular cereal manufacturer that the mean weight of cereal in the boxes is less than 300g. A sample of 50 boxes yields a sample mean weight of 296g. Assume that the population standard deviation is 5g.
a) Can we conclude that the claim is true? Test at α = 0.05.
b) Obtain a 95% confidence interval for μ.
3. The time taken to assemble a car in a certain plant has a normal distribution with mean of 25.4 hours and a standard deviation of 4.1 hours. Calculate the probability that a car can be assembled at this plant in the following period of time:
a) More than 28.8 hours
b) Between 18.6 and 27.5 hours
c) Between 25.0 and 34.0 hours