Question $1$:

As the site engineer at a large construction site, you have been asked to oversee the concrete production

process. You are particularly worried about the slump of the concrete. If the slump is too small, it

suggests the concrete is too stiff. If there is too much slump, then the concrete is too watery. The contract

specifications state that the slump for the particular concrete used should be $1$ inch, with a $90\%$ level of

confidence. Therefore, during the concrete production process, you instruct the laboratory technician to

take $20$ random samples of fresh concrete and measure the slump using the appropriate test equipment.

The technician obtained the following test results $($in inches$)$:

Would you accept that day's production of concrete at the given level of confidence? Assume that, from

past slump test results, the concrete slumps are known to be normally distributed.