Suppose that in the preceding exercise the first measurement is recorded incorrectly as 16.0 instead of 14.5. Show that, even though the mean of the sample increases to \(\bar{x}=14.7\), the null hypothesis \(H_{0}: \mu=\) 14.0 is not rejected at level \(\alpha=0.05\). Explain the apparent paradox that even though the difference between observed \(\bar{x}\) and \(\mu\) has increased, the null hypothesis is no longer rejected.

Data From Preceding Exercise

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Determining a joint cumulative distribution function Find the joint cumulative distribution function of the two random variables of the preceding exercise, and use it to find the probability that both random variables will take on values less than 1.