Question 3 A researcher from Department of Industrial Engineering is conducting a research about the measurement...

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Question 3 A researcher from Department of Industrial Engineering is conducting a research about the measurement of tire performance of a sport bike. One very important measure of tire performance is the strength index, which indicates the tire's resistance with a tire graded with a base of 100. This means that a tire with a grade of 300 should last three times as long, on average, as a tire graded with a base of 100. Consumer council wants to estimate the actual strength index of a brand name of tires that claims "graded 300" on the sidewall of the tire. A random sample of n=18 indicates a sample mean strength index of 195.3 and a sample standard deviation of 21.4. a) Assuming that the population of strength indexes is normally distributed, construct a 95% confidence interval estimate of the population mean of strength index for tires produced by this manufacturer under this brand name. Assume historical information gives population standard deviation =21.4. b) Assuming that the population of strength indexes is normally distributed, construct a 95% confidence interval estimate of the population mean of strength index for tires produced by this manufacturer under this brand name. c) Do you think that the consumer council should accuse the manufacturer of producing tires that do not meet the performance information provided on the sidewall of the tire? Explain. d) Explain why an observed strength index of 210 for a particular tire is not unusual, even though it is outside the confidence interval developed in (a). e) Assuming that the population of strength indexes is normally distributed, assume historical information gives population standard deviation =21.4. You are interested in testing whether the population mean strength is poorer than "graded 300". a. State the Ho and H b. Let significance level = 0.05. If the p-value is written as the form of P(Z>g). Find g. Question 3 A researcher from Department of Industrial Engineering is conducting a research about the measurement of tire performance of a sport bike. One very important measure of tire performance is the strength index, which indicates the tire's resistance with a tire graded with a base of 100. This means that a tire with a grade of 300 should last three times as long, on average, as a tire graded with a base of 100. Consumer council wants to estimate the actual strength index of a brand name of tires that claims "graded 300" on the sidewall of the tire. A random sample of n=18 indicates a sample mean strength index of 195.3 and a sample standard deviation of 21.4. a) Assuming that the population of strength indexes is normally distributed, construct a 95% confidence interval estimate of the population mean of strength index for tires produced by this manufacturer under this brand name. Assume historical information gives population standard deviation =21.4. b) Assuming that the population of strength indexes is normally distributed, construct a 95% confidence interval estimate of the population mean of strength index for tires produced by this manufacturer under this brand name. c) Do you think that the consumer council should accuse the manufacturer of producing tires that do not meet the performance information provided on the sidewall of the tire? Explain. d) Explain why an observed strength index of 210 for a particular tire is not unusual, even though it is outside the confidence interval developed in (a). e) Assuming that the population of strength indexes is normally distributed, assume historical information gives population standard deviation =21.4. You are interested in testing whether the population mean strength is poorer than "graded 300". a. State the Ho and H b. Let significance level = 0.05. If the p-value is written as the form of P(Z>g). Find g.