Task:

$1.$ Data Collection:

Use the provided concrete compressive strength data for four weeks.

Week $1$: $\{32\mathrm{.}1,32\mathrm{.}5,31\mathrm{.}8,33\mathrm{.}2,32\mathrm{.}0,32\mathrm{.}7,31\mathrm{.}5,32\mathrm{.}3,32\mathrm{.}9,32\mathrm{.}1\}$

Week $2$: $\{31\mathrm{.}9,32\mathrm{.}3,32\mathrm{.}7,33\mathrm{.}0,32\mathrm{.}4,32\mathrm{.}8,31\mathrm{.}6,32\mathrm{.}2,33\mathrm{.}1,32\mathrm{.}0\}$

Week $3$: $\{32\mathrm{.}2,32\mathrm{.}6,31\mathrm{.}7,32\mathrm{.}9,32\mathrm{.}3,31\mathrm{.}5,32\mathrm{.}8,32\mathrm{.}1,31\mathrm{.}9,33\mathrm{.}0\}$

Week $4$: $\{32\mathrm{.}5,31\mathrm{.}8,32\mathrm{.}3,32\mathrm{.}7,32\mathrm{.}0,33\mathrm{.}2,31\mathrm{.}6,32\mathrm{.}9,32\mathrm{.}1,32\mathrm{.}4\}$

$2.$ Calculations:

$$ Calculate the average and standard deviation for each week's data.

$3.$ Control Chart Creation:

$$ Use Excel to create a control chart.

$$ Include the following elements:

$$ Data points for each week.

$$ Centerline $($CL$)$ representing the average compressive strength

$$ Upper Control Limit $($UCL$)$ and Lower Control Limit $($LCL$)$ calculated using

CL$=$x$\backslash$pm $3$s

$4.$ Analysis:

$$ Analyze the control chart to identify any points beyond the control limits$.$

$$ Look for patterns or trends in the data.

$5.$ Submission:

$$ Submit the control chart and analysis report on Canvas.

Note: use a significance level of $0\mathrm{.}05,$ and therefore, the critical z$-$value for a two$-$tailed test should

be taken from Cumulative Standard Normal Distribution Table given in previous lecture.