10. An engineer uses an analytical procedure for measuring reliability. This procedure produces results that exhibit...

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10. An engineer uses an analytical procedure for measuring reliability. This procedure produces results that exhibit a standard deviation of 0.04. It is desired that there be a 95% chance of obtaining an estimate within 0.01 of the true mean. What sample size is required? 11. The measurement process on the lengths of parts produced follows a normal distribution. A sample of ten parts produced a mean length of 1.001 mm. The population standard deviation is 0.0310 mm. Find a 98% confidence interval for the actual mean length of parts produced. 12. A random sample of 100 recorded deaths in the United States during the past year showed an average life span of 74.0 years. Assuming a population standard deviation of 8.91 years, does this seem to indicate that the average life span today is less than 75.0 years? Use a 0.05 level of significance. 13. Suppose that a study is to be conducted to determine the percentage of days on which a particular machine is likely to breakdown. This unknown percentage is to be estimated with the corresponding percentage in a sample of cases. a) How many cases should be studied in order to have a 90% chance that the estimate will be within two percentage points of the true percentage? b) If prior studies indicate that the percentage is approximately 10%, how many cases must be studied to have a 90% chance that the estimate will be within two percentage points of the true value? 14. As a manufacturer you want to pay out warranties on only 10.5% of your product. If you honour warranties on more that 10.5%, your profit margin falls below acceptable levels. If you end up honouring less that 10.5% of your warranties, then you could make a stronger guarantee and charge more for it. An analysis of the last year indicates that on the sale of 1500 units of a particular product, the warrantee was honoured on 187 of them. At a 4% level of significance, does this indicate that the warrantee period should be changed? 15. Radon is a colourless, odourless gas that is naturally released by rocks and soils and may concentrate in tightly closed houses. University researchers placed detectors in 12 homes in a particular suburb and the readings were 91.9 103.8 97.8 99.6 111.4 122.3 105.4 95.0 96.6 119.3 104.8 101.7 Is there evidence at the 5% level that the mean reading of all the homes in the suburb is more than 98.5? 10. An engineer uses an analytical procedure for measuring reliability. This procedure produces results that exhibit a standard deviation of 0.04. It is desired that there be a 95% chance of obtaining an estimate within 0.01 of the true mean. What sample size is required? 11. The measurement process on the lengths of parts produced follows a normal distribution. A sample of ten parts produced a mean length of 1.001 mm. The population standard deviation is 0.0310 mm. Find a 98% confidence interval for the actual mean length of parts produced. 12. A random sample of 100 recorded deaths in the United States during the past year showed an average life span of 74.0 years. Assuming a population standard deviation of 8.91 years, does this seem to indicate that the average life span today is less than 75.0 years? Use a 0.05 level of significance. 13. Suppose that a study is to be conducted to determine the percentage of days on which a particular machine is likely to breakdown. This unknown percentage is to be estimated with the corresponding percentage in a sample of cases. a) How many cases should be studied in order to have a 90% chance that the estimate will be within two percentage points of the true percentage? b) If prior studies indicate that the percentage is approximately 10%, how many cases must be studied to have a 90% chance that the estimate will be within two percentage points of the true value? 14. As a manufacturer you want to pay out warranties on only 10.5% of your product. If you honour warranties on more that 10.5%, your profit margin falls below acceptable levels. If you end up honouring less that 10.5% of your warranties, then you could make a stronger guarantee and charge more for it. An analysis of the last year indicates that on the sale of 1500 units of a particular product, the warrantee was honoured on 187 of them. At a 4% level of significance, does this indicate that the warrantee period should be changed? 15. Radon is a colourless, odourless gas that is naturally released by rocks and soils and may concentrate in tightly closed houses. University researchers placed detectors in 12 homes in a particular suburb and the readings were 91.9 103.8 97.8 99.6 111.4 122.3 105.4 95.0 96.6 119.3 104.8 101.7 Is there evidence at the 5% level that the mean reading of all the homes in the suburb is more than 98.5?