Insurance companies are interested in knowing the mean weight of machine; they believe it is 3000 pounds. To see if that assumption is correct, they checked a random sample of 101 machines. For that group the mean weight was 2867 pounds, with standard deviation of 541.8 pounds. Perform a test at α=0.01 to determine if the true mean weight of all machines is different than 3000 pounds.
Question: State hypotheses, find the test statistic and critical value, and state conclusion. (3 decimal round)