Final Answer:
To conclude at a 10% significance level that the two departments differ in unit cost variance based on the given data, we need a calculated test statistic exceeding 1.746. However, due to the limited sample size (n=16), the test statistic is insufficient to draw such a conclusion.
Step-by-step explanation:
To determine if the observed difference in variances is statistically significant, we can perform a Levene's test. This test compares the variances of two populations based on the absolute deviations from the medians of their respective samples.
Calculate the pooled variance:
First, pool the variances: Sp = [(n1-1)*s1^2 + (n2-1)*s2^2] / (n1+n2-2)
Sp = [(16-1)*2.3^2 + (16-1)*5.4^2] / (16+16-2)
Sp ≈ 15.18
Calculate the test statistic:
L = (n1 + n2 - 2) * (Sn1^2 - Sn2^2) / Sp
L = (16 + 16 - 2) * ((2.3^2) - (5.4^2)) / 15.18
L ≈ 1.48
Compare the test statistic to the critical value:
At a 10% significance level (α = 0.10) and equal sample sizes (n1 = n2), the critical value for Levene's test is approximately 1.746.
Since the calculated test statistic (L ≈ 1.48) is lower than the critical value (1.746), we cannot statistically conclude that the two production departments differ in terms of unit cost variance at the 10% significance level.
However, it's important to note that the limited sample size (n=16) reduces the power of the test to detect potential differences. A larger sample size could potentially lead to a statistically significant result.
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Complete Question
The accounting department analyzes the variance of the weekly unit costs reported by two 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 a = .10.
Calculate the value of the test statistic (to 2 decimals).
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