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Stable cost reporting in a manufacturing setting is typically a sign that operations are running smoothly. The accounting department at Rockwell Collins, an avionics manufacturer, analyzes the variance of the weekly costs reported by two of its production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.3 and 5.4, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use α = 0.10 (to 2 decimals).

Sagot :

Answer:

Following are the responces to the given question:

Step-by-step explanation:

For this issue the statistical programme performance is:

Two overview hypothesis test sample variance:

[tex]\to \sigma_1^2[/tex]  =Population variance 1

[tex]\to \sigma_2^2[/tex] = Population variance 2

[tex]\to \frac{\sigma_1^2}{\sigma_2^2}=[/tex] Two variance ratios

[tex]\to H_0: \frac{\sigma_1^2}{\sigma_1^2}=1\\\\\to H_A: \frac{\sigma_1^2}{\sigma_1^2}\neq 1[/tex]

Following are the result of the Hypothesis test: [tex]Ratio \ \ \ \ \ \ \ \ \ \ Num.DF \ \ \ \ \ \ \ \ \ \ Den.DF \ \ \ \ \ \ \ \ \ Sample\ \ Ratio\ \ \ \ \ \ F-Stat \ \ \ \ \ \ \ P-value\\\\[/tex]

[tex]\frac{\sigma_1^2}{\sigma_1^2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.3478261 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.3478261 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1091[/tex]

Test statistic [tex]= 2.3478 \approx 2.35[/tex]

P-value > 0.10

The null hypothesis should not be rejected.

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