Reference no: EM132844653

Ten cans of stewed tomatoes were removed at random from a population of 1,000 cans. The drained weight of the contents were shown in the table left. It is known that the population of drained weights is normally distributed with a standard deviation of 0.82.

a) These cans are supposed to contain 410 g of drained tomatoes. Suppose the operator of the machine that fills the tins has reason to believe that the average weight of the tins is under this stated amount. This is bad for business because they may get complaints from consumers. Conduct an appropriate test of hypothesis to prove whether this is the case. Use α= 0.01.

- state appropriate hypothesis

- calculate the test statistic by hand

- find corresponding p-value from z-table to your test statistic value

- confirm your results by running the appropriate test in MiniTab

- write clear conclusions.

b) Calculate by hand the 99% confidence interval for the mean weight of the entire population of canned tomatoes filled by this machine. Does the confidence interval constructed support your conclusions from part 'a'? Explain.