The dispersion, or variance, of haul times on a construction project is of great importance to the project

supervisor, because highly variable haul times cause problems in scheduling jobs. The supervisor of

the truck crews states that the range of haul times should not exceed $40$ minutes $($The range is the

difference between the longest and shortest times.$)$ Assuming these haul times to be approximately

normally distributed, the project supervisor takes the statement on the range to mean that the standard

deviation $(\backslash$sigma should be approximately $10$ minutes$).$ Fifteen haul times are actually measured and show

a mean of $142$ minutes and a standard deviation of $12$ minutes. Can the claim of $\backslash$sigma $=10$ be refuted at the

$5\%$ significance level?