7. When companies employ control charts to monitor the quality of their products, a series of small samples is typically used to determine if the process is "in control" during the period of time in which each sample is selected. Suppose a concrete-block manufacturer samples nine blocks per hour and tests the breaking strength of each. During one-hour’s test, the mean and standard deviation are 985.6 pounds per square inch (psi) and 22.9 psi, respectively. a. Construct a 99% confidence interval for the mean breaking strength of blocks produced

Answer:A 99% confidence interval for the mean breaking strength of blocks produced is [tex][959.987, 1011.213][/tex]Step-by-step explanation:A (1 - [tex]\alpha[/tex])x100% confidence interval for the average break in these conditions It is an interval for the population mean with unknown variance and is given by:[tex][\bar x -T_{(n-1,\frac{\alpha}{2})} \frac{S}{\sqrt{n}}, \bar x +T_{(n-1,\frac{\alpha}{2})} \frac{S}{\sqrt{n}}][/tex][tex]\bar X = 985.6psi[/tex][tex]n = 9[/tex][tex]\alpha = 0.01[/tex][tex]T_{(n-1,\frac{\alpha}{2})}=3.355[/tex][tex]S = 22.9[/tex]With this information the interval is determined by:[tex][985.6 - 3.355\frac{22.9}{\sqrt{9}}, [985.6 - 3.355\frac{22.9}{\sqrt{9}}] = [959.987, 1011.213] [/tex]