The Table Below Shows the Data from Samples of Size $n=5$

question 7

Essay

The table below shows the data from samples of size $n=5$ randomly chosen from the outputs of a process on 20 different days. Assume the specification limits are USL $=2.1$ and $\mathrm{LSL}=5.7$ .


$\begin{array}{cccccc}\hline \text { Sample } & & {\text { Data }} \\\hline 1 & 4.5 & 2.1 & 5.4 & 2.7 & 4.5 \\2 & 3.6 & 3.5 & 6.1 & 4.9 & 4.2 \\3 & 5.1 & 6.2 & 2.4 & 3.7 & 5.1 \\4 & 4.9 & 5.4 & 3.5 & 5.4 & 3.7 \\5 & 4.1 & 3.8 & 3.8 & 4.6 & 4.9 \\6 & 3.7 & 4.6 & 4.8 & 4.2 & 5.2 \\7 & 5.6 & 4.7 & 4.1 & 5.1 & 3.1 \\8 & 4.8 & 5.1 & 4.3 & 4.6 & 2.7 \\9 & 6.1 & 4.6 & 4.7 & 3.8 & 4.2 \\10 & 2.4 & 4.8 & 5.6 & 4.1 & 4.8 \\11 & 3.7 & 5.3 & 2.9 & 4.7 & 6.3 \\12 & 4.5 & 3.4 & 3.4 & 5.2 & 4.5 \\13 & 5.2 & 2.7 & 5.1 & 6.2 & 2.9 \\14 & 3.4 & 5.5 & 4.6 & 2.4 & 3.4 \\15 & 4.8 & 3.6 & 4.8 & 4.4 & 4.6 \\16 & 4.1 & 4.6 & 4.9 & 4.9 & 4.3 \\17 & 4.6 & 3.7 & 3.5 & 3.7 & 5.2 \\18 & 5.1 & 4.2 & 5.6 & 4.1 & 5.7 \\19 & 3.7 & 4.8 & 4.9 & 2.3 & 4.5 \\20 & 5.4 & 3.9 & 4.2 & 5.4 & 4.3 \\\hline\end{array}$
a. Assuming the process is under control, construct a capability analysis diagram for the process.
b. Find the percentage of data items that fall outside the specification limits.
c. Is the process capable? Support your answer with a numerical measure of capability.

Identify phases within the business cycle.

Analyze economic indicators to deduce periods of recession, prosperity, deflation, disinflation, or inflation.

Calculate changes in the Consumer Price Index (CPI) and understand their economic implications.

Understand the relationship between unemployment rates, inflation, and cyclical unemployment.

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