Exercise $7-39$ Algo

Random samples of size $n=380$ are taken from a population with $p=0\mathrm{.}06.$

a$.$ Calculate the centerline, the upper control limit $($UCL$),$ and the lower control limit $($LCL$)$ for the $\frac{?}{\text{b}\text{a}\text{r}}(p)$ chart. $($Round the value for the centerline to $2$ decimal places and the values for the UCL and LCL to $3$ decimal places.$)$

$\backslash$table$[[,],[$Centerline$,],[$Upper Control Limit,$],[$Lower Control Limit,$]]$

b$.$ Calculate the centerline, the upper control limit $($UCL$),$ and the lower control limit $($LCL$)$ for the $\frac{?}{\text{b}\text{a}\text{r}}(p)$ chart if samples of $260$ are used. $($Round the value for the centerline to $2$ decimal places and the values for the UCL and LCL to $3$ decimal places.$)$

$\backslash$table$[[,],[$Centerline$,],[$Upper Control Limit,$],[$Lower Control Limit,$]]$

c$.$ Discuss the effect of the sample size on the control limits$.$

The control limits have a

spread with smaller sample sizes due to the standard error for the smaller sample size.