7 A mill owner claims that the mean mass of sacks of flour produced at his mill is 51 kg . A quality control officer suspects that the mean mass is actually less than 51 kg . In order to test the owner's claim she finds the mass, \(x \mathrm {~kg}\), of each of a random sample of 150 sacks and her results are summarised as follows.
$$n = 150 \quad \Sigma x = 7480 \quad \Sigma x ^ { 2 } = 380000$$
- Carry out the test at the \(2.5 \%\) significance level.
You may now assume that the population standard deviation of the masses of sacks of flour is 6.856 kg . The quality control officer weighs another random sample of 150 sacks and carries out another test at the 2.5\% significance level. - Given that the population mean mass is 49 kg , find the probability of a Type II error.
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