A firm sells detergent packed in two plants. From past experience, the firm knows that the amount of detergent in the boxes packed in the two plants is normally distributed.
The firm takes a random sample of 25 boxes from the output of each plant and finds that the mean weight and standard deviation of the detergent in the boxes from plant 1 is 1064 g (2.34 lb) and 100 g, respectively. For the sample in plant 2, the mean is 1024 g and the standard deviation is 60 g.
- Can the firm claim with a 95% level of confidence that the boxes of detergent from plant 1 contain more than 1000 g?
- Test at the 95% level of confidence that the amount of detergent in the boxes of both plants is the same.