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# As a manager of an airline company you want to learn the average weight of luggages checked in on a flight. From a sample of

As a manager of an airline company you want to learn the average weight of luggages checked in on a flight. From a sample of $16$ luggages, you find the average to be $26$ kg and the standard deviation to be $12$ kg$.$ The person in charge of the luggages argues that the population mean is exactly $32$ kg$.$

a$.\text{}\backslash "">(6)$ Test the hypothesis at $5\%$ significance level.

b$.\text{}\backslash "">(6)$ Calculate a $95\%$ confidence interval.

c$.\text{}\backslash "">(8)$ If the true mean is $23$ kg what can you say about the probability of type II error

$($make an assessment to the extent which statistical tables allow$)?$

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