An energy drink company routinely measures the caffeine content of their drinks.

Question

An energy drink company routinely measures the caffeine content of their drinks. Suppose that the complay
selects 100 samples of the drink every hour from it's production line and determines the caffeine content.
From previous analyses, the company is confident that the caffeine content has a normal distribution with standard deviation = 6.8mg. During a one hour period, the 100 samples yielded a mean cafeine content of x = 130mg

Suppose the company repeats this process every hour of every day for one week, thus constructing 40
separate confidence intervals for the estimated mean caffeine content of their drinks. Of these intervals,
how many would you expect to fail to contain the value of the u thus providing an inaccurate estimation
of the mean caffeine content?

Explanation / Answer

If it is a 95% confidence interval, then we expect the mean to fall out of this interval 5% of them time.

Thus, 5% of 40 = 2.

This means that out of 40 samples, expect 2 of them to fail to contain the value of the u. [ANSWER, 2, if 95% confidence]

In general, if c = the confidence level, we expect

40(1-c) would fail. [ANSWER, in general for any c]

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