Experience has shown that 20% of manufactured products are of top-quality. In today's production of 400 articles only 50 are of top quality. Show that either the production of the day chosen was not a representative sample or the hypothesis of 20% was wrong. Based on the particular days production find also the 95% confidence limits for the percentage of top quality product. 2. The fatality rate of typhoid patients is believed to be 17.26 percent. In a certain year 640 patients suffering from typhoid were treated in a metropolitan hospital and only 63 patients died. Can you consider the hospital efficient? 3. In a sample of 1000 people in Maharashtra 540 are rice eaters and the rest are wheat eaters. Can we assume that the both rice and wheat eaters are equally popular in this state at 1% level of significance? 4. In a big city 325 men out of 600 men were found to be smokers. Does this information support the conclusion that the majority of men in this city are smokers? 5. In a large city A 20% of random sample of 900 school boys had a slight physical defect. In another large city B 18.5% of a random sample of 1600 school boys had the same defect. Is the difference between the proportions significant? 6. During a country wide investigation the incidence of TB was found to be 1%. In a college of 400 strength, 5 were reported to be affected whereas in another college of 1200 strength 10 were reported to be affected. Does this indicate any significant difference? 7. A company has the head office at Calcutta and a branch at Bombay. The personal director wanted to know if the workers at the two places would like the introduction of a new plan of work and a survey was conducted for this purpose. Out of a sample of 500 workers at Calcutta, 62% favoured the new plan. At Bombay out of a sample of 400 workers 41% were against the new plan. Is there any significant difference between the two groups in their attitude towards the new plan at 5% level? S. A manufacturer of ball pens claims that a certain pen be manufactures has a mean writing life of 400 pages, with a standard deviation of 20 pages. A purchasing agent selects a sample of 100 pens and puts them for test. The mean writing life for the sample was 390 pages. Should the purchasing agent reject the manufacture's claim at 5% level? 9. A random sample of 200 tins of coconut oil gave an average weight of 4.95 kg, with a standard deviation of 0.21 kg. Do we accept that net weight is 5kg per tin at 5% los. 10. An insurance agent has claimed that the average age of policy holders who insure through him is less than the average for all agents which is 30.5 years. A random sample of 100 policy holders who had insured through him reveals that the mean and 3.d are 28.8 and 6.35years respectively. Test the claim at 5% level of significance