Question

1. Suppose you are supervising two production lines of a smartphone assembly plant. The time for every worker to assemble a single smartphone can be assumed to be normally distributed. You are interested in knowing the variations in the assembly time from worker to worker. In particular, you are interested if there is any significant difference in the variance of assembly time between the two production lines. If any one of the two lines yields a significantly larger variance, you will assign workers from that line for further training. Two random samples of workers were taken from the two production lines and their assembly time were recorded. The summary data follow: Production line 1 Production line 2 Sample standard deviation (in hours) 1.32825 0.76863 Sample size 10 25 Conduct a statistical test to determine whether these is any significant difference in the assembly time variances. You should follow the instructions below precisely to get full marks: state clearly the null and alternative hypotheses (in both symbols and words), use a significance level of a = 2%, compute the value of the test statistic, then use the critical value method to make a decision. Then provide 2–3 lines for your conclusions. (6 marks)

Answer 1

S2 = 0.76863 S, = 1.32 825, ni = 10, n2 = 25 ** Null hypothesis, Ho: 0,2 = 0 Alternative hypothesis, Ha: 01 + 02? Siz 1.32825 ** Test Statistic, F = G = 0.768632 = 2.9862 ** Q=0.02,5=0.01, 1-9 = 0.99 of, = 10-1=9, df2 = 25-1 = 24 critical values are : Foyz, df,,df2. F1-hyp, dfuldfy = Fo.o, 9,24 F0.99,9,24 = 3.256, 0.211 The rejection regions are : F <0.211 or C F > 3. 256 ** Since our test statistic is inside the interval 10.211, 3.256), the test Statistic does not fall on the rejection regions, so we fail to reject the null hypothesis. We conclude that there is no significant difference in the assembly time variances. **