## Related questions with answers

(Use Excel) Color coding is often used in manufacturing operations to display production status or to identify/prioritize materials. For example, suppose "green" status indicates that an assembly line is operating normally, "yellow" indicates it is down waiting on personnel for set up or repair, "blue" indicates it is down waiting on materials to be delivered, and "red" indicates an emergency condition. Management has set realistic goals whereby the assembly line should be operating normally 80% of the time, waiting on personnel 9% of the time, waiting on materials $9 \%$ of the time, and in an emergency condition 2% of the time. Based on $250$ recent status records, the status was green $185$ times, yellow $24$ times, blue $32$ times, and red $9$ times.

a. State the appropriate null and alternative hypotheses to test if the proportions of assembly line statuses differ from the goals set by management.

b. Calculate the value of the test statistic.

c. Use Excel's CHISQ.DIST.RT function to calculate the $p$-value.

d. Are management's goals being met at $\alpha=0.05$ ? Will your conclusion change at $\alpha=0.01$ ?

Solution

Verified$\bold{a.)}$ The null hypothesis states that

$H_0:\text{The assembly line status proportions don't differ from the management goals.}$

so the alternative hypothesis will be the opposite.

$H_A:\text{The assembly line status proportions differ from the management goals.}$

The predicted values is equal to the proportion multiplied to $n$. So in Mathematical terms, the null hypotheses is

$H_0: p_1=0.80, p_2=0.09, p_3=0.09, p_4=0.02.$

and the Alternative hypotheses is

$H_a: p_1\ne0.80 \text{ or } p_2\ne0.09 \text{ or } p_3\ne0.09 \text{ or } p_3\ne0.02.$

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