A machine puts out 16 imperfect articles in a batch of 500. After the machine is overhauled it puts out 3 imperfect articles in a batch of 100. Has the machine improved? 3. A quality control manager in a Measure Ruler company is examining the metric rulers. Each ruler is supposed to be 100 cm long. The data of 100 samples gave a sample mean 99.9 cm with variance 0.0036 cm. Should the manager recalibrate the machine? 4. Test the hypothesis that there is no difference in quality of four brands of tyres A, B, C, and D based on the data given below. Use 5% level of significance. Lasted 60000 km A 26 118 56 B 23 93 84 C 15 116 69 D 32 121 47 5. It is believed that glucose treatment will extend the sleep time of mice. In an experiment 10 mice that are selected at random and given glucose treatment are found to have a mean hexabarbital sleep time of 47.2 min with a standard deviation of 9.3 min. A further sample of 11 untreated mice are found to have mean hexabarbital sleep time of 28.5 min with a standard deviation of 7.2 min. At 1% level are these results significant evidence in favour of the hypothesis ?