Ten Samples of Size Four Were Taken from a Process

question 80

Essay

Ten samples of size four were taken from a process, and their weights measured. The sample averages and sample ranges are in the following table. Construct and plot an x-bar and R-chart using this data. Is the process in control?
$$\begin{array} { |l | l | l | } \hline \text { Sample } & \text { Mean } & \text { Range } \\\hline 1 & 20.01 & 0.45 \\\hline 2 & 19.98 & 0.67 \\\hline 3 & 20.25 & 0.30 \\\hline 4 & 19.90 & 0.30 \\\hline 5 & 20.35 & 0.36 \\\hline 6 & 19.23 & 0.49 \\\hline 7 & 20.01 & 0.53 \\\hline 8 & 19.98 & 0.40 \\\hline 9 & 20.56 & 0.95 \\\hline 10 & 19.97 & 0.79 \\\hline\end{array}$$

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Definitions:

Aggregate Demand

The total demand for all goods and services within an economy at various price levels, in a given time period.

Expansionary Gap

A situation where the actual economic output exceeds the potential output, often leading to inflation.

Short-Run Aggregate Supply

This is the total supply of goods and services that firms in an economy plan on selling during a short time period, taking into account current prices.

Government Spending

The total expenditure by the government on goods and services, including public services, infrastructure, and welfare programs, to influence the economy.