Refer to Exercise 7.1 where a construction engineer recorded the quantity of gravel (in metric tons) used in concrete mixes. The quantity of gravel for \(n=24\) sites has \(\bar{x}=5,818\) tons and \(s^{2}=7,273,809\) so \(s=\) 2,697 tons.

(a) Construct a test of hypotheses with the intent of showing that the mean gravel usage in the concrete mix is less than 5,800 tons. Take \(\alpha=0.10\).

(b) Based on your conclusion in part (a), what error could you have made? Explain in context of the problem.

Data From Exercise 7.1

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7.1 A construction engineer collected data from some con- struction sites on the quantity of gravel (in metric tons) used in mixing concrete. The quantity of gravel for n = 24 sites 4861 5158 8642 2896 7654 9891 8381 6215 1116 7918 2313 8114 3517 8852 5712 4312 8023 1215 3598 2429 8211 4613 9168 6819 has x=5818 tons and s = 2697 tons. What can one assert with 90% confidence about the maximum error if x = 5818 tons is used as a point estimate of the true population mean amount of gravel used in con- crete mixes?