A systems engineer is monitoring the latency of a high-speed data link. The latency, in milliseconds (ms), is known to follow a normal distribution with a standard deviation of 2.5 ms. Under optimal conditions, the mean latency, μ\muμ, is 14.5 ms.
The engineer suspects that the link is degrading and the mean latency has increased. To investigate this, she takes a random sample of 10 latency measurements and performs a hypothesis test at the 10% significance level.
She tests the null hypothesis H0:μ=14.5H_0: \mu = 14.5H0:μ=14.5 against the alternative hypothesis H1:μ>14.5H_1: \mu > 14.5H1:μ>14.5.
While recording the data, one of the measurements was corrupted. The remaining 9 measurements are:
15.1,13.8,16.4,14.9,17.2,12.5,15.8,14.3,16.1 15.1, \quad 13.8, \quad 16.4, \quad 14.9, \quad 17.2, \quad 12.5, \quad 15.8, \quad 14.3, \quad 16.1 15.1,13.8,16.4,14.9,17.2,12.5,15.8,14.3,16.1Given that the test resulted in the rejection of H0 H_0\,H0 at the 10% level of significance, determine the minimum possible value of the corrupted data point, xxx. Give your answer to 1 decimal place.
