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- Long-distance runners have contended that moderate exposure to ozone increases lungcapacity. To investigate this possibility, a researcher exposed 12 rats to ozone at the rateof 2 parts per million for a period of 30 days. The lung capacity of rats was determined atthe beginning of the study and again after the 30 days of ozone exposure. The lungcapacities (in mL) are given here:(a) If we can assume normality, is there sufficient evidence to support the conjecture thatozone exposure increases lung capacity? Use α = 0.01? b) Estimate the size of the increase in lung capacity after exposure to ozone. Use a 99%confidence interval.The specification for the pull strength of a wire that connects an integrated circuit to its frame is 10 g or more. Units made with aluminum wire have a defect rate of 10%. A redesigned manufacturing process, involving the use of gold wire, is being investigated. The goal is to reduce the rate of defects to 5% or less. Out of the first 100 units manufactured with gold wire, only 4 are defective. True or false: a) Since only 4% of the 100 units were defective, we can conclude that the goal has been reached. b) Although the sample percentage is under 5%, this may represent sampling variation, so the goal may not yet be reached. c) There is no use in testing the new process, because no matter what the result is, it could just be due to sampling variation. d) If we sample a large enough number of units, and if the percentage of defective units is far enough below 5%, then it is reasonable to conclude that the goal has been reached.A researcher is testing the effect of a new cold and flu medication on reaction time. A sample of n = 16 students is obtained and each student is given the normal dose of the medicine. Thirty minutes later, each student's reaction time is measured. The scores for the sample averaged M = 220 milliseconds with SS = 6000. Assuming that reaction time for students in the regular population averages μ = 200 milliseconds, are the data sufficient to conclude that the medication has a significant effect on reaction time? Test at the .05 level of significance. Make a point estimate and a 95% confidence interval estimate for the treated population mean.
- Suppose the incidence rate of myocardial infarction (MI)was 5 per 1000 among 45- to 54-year-old men in 2000.To look at changes in incidence over time, 5000 men in thisage group were followed for 1 year starting in 2010. Fifteennew cases of MI were found. Suppose that 25% of patients with MI in 2000 died within24 hours. This proportion is called the 24-hour case-fatalityrate. >Suppose we eventually plan to accumulate 50 MIcases during the period 2010–2015. Assume that the24-hour case-fatality rate is truly 20% during this period.How much power would such a study have in distinguishingbetween case-fatality rates in 2000 and 2010–2015 if atwo-sided test with significance level .05 is planned?An experiment has been conducted to evaluate a new process for producing syntheticdiamonds. A number of diamonds have been generated by the new process with recordedweights of 0.46, 0.61, 0.52, 0.48, 0.57, and 0.54 carat. A study of the process costsindicates that the actual average weight of the diamonds must exceed 0.5 in order that theprocess be operated at a profitable level. a). At 5% level of significance, is there sufficient evidence to conclude that the process isoperating at a profitable level? Your conclusion must be in terms of the P-Value aswell as setting up a Rejection Region. You must show all necessary work. b). Which statistical distribution should be applied in this situation and why? Explaincarefully. c). What type of error is possible and describe this error in terms of the problemAn experiment has been conducted to evaluate a new process for producing syntheticdiamonds. A number of diamonds have been generated by the new process with recordedweights of 0.46, 0.61, 0.52, 0.48, 0.57, and 0.54 carat. A study of the process costsindicates that the actual average weight of the diamonds must exceed 0.5 in order that theprocess be operated at a profitable level.a). At 5% level of significance, is there sufficient evidence to conclude that the process isoperating at a profitable level? Your conclusion must be in terms of the P-Value aswell as setting up a Rejection Region. You must show all necessary work.b). Which statistical distribution should be applied in this situation and why? Explaincarefully.c). What type of error is possible and describe this error in terms of the problem.d). Based on a 95% confidence level, estimate the actual mean weight of syntheticdiamonds using the new process.e). Carefully interpret this interval estimation.f). Explain carefully whether…
- Suppose the incidence rate of myocardial infarction (MI)was 5 per 1000 among 45- to 54-year-old men in 2000.To look at changes in incidence over time, 5000 men in thisage group were followed for 1 year starting in 2010. Fifteennew cases of MI were found. Q.)Suppose that 25% of patients with MI in 2000 died within24 hours. This proportion is called the 24-hour case-fatalityrate. 7.14 Of the 15 new MI cases in the preceding study,5 died within 24 hours. Test whether the 24-hour casefatality rate changed from 2000 to 2010. 7.15 Suppose we eventually plan to accumulate 50 MIcases during the period 2010–2015. Assume that the24-hour case-fatality rate is truly 20% during this period.How much power would such a study have in distinguishingbetween case-fatality rates in 2000 and 2010–2015 if atwo-sided test with significance level .05 is planned? 7.16 How large a sample is needed in Problem 7.15 toachieve 90% power?Suppose the incidence rate of myocardial infarction (MI)was 5 per 1000 among 45- to 54-year-old men in 2000.To look at changes in incidence over time, 5000 men in thisage group were followed for 1 year starting in 2010. Fifteennew cases of MI were found. Suppose that 25% of patients with MI in 2000 died within24 hours. This proportion is called the 24-hour case-fatalityrate.7.14 Of the 15 new MI cases in the preceding study,5 died within 24 hours. Test whether the 24-hour casefatality rate changed from 2000 to 2010.Fluoride Exposure in Drinking WaterExercise 2.250 introduces a study showing thatfluoride exposure might have long-term negativeconsequences for the offspring of pregnant women.Part of the study examines the effect of adding flu-oride to tap water on mean fluoride concentrationin women. Summary statistics for fluoride concen-tration (measured in mg/L) for the two groups are given in Table 6.17. Find and interpret a 99% con-fidence interval for the mean increase in fluorideconcentration for those with fluoridated tap water. 1. find the t-score enter positive z-score 2. find the standard of error round 4 decimal places. 3 find the margin of error round 4 decimal places
- Table 1 shows the total amount spent in Malaysia by tourists from Saudi Arabia and Japan from 2010 to 2019. Based on Table 1, at the 0.01 level of significance, can we conclude that tourists from Saudi Arabia spent less than those from Japan. Table 1: Amount spend by tourists from Saudi Arabia and Japan Year Saudi Arabia Jepun 2010 0.7 1.1 2011 0.7 1.1 2012 0.8 1.4 2013 0.8 1.5 2014 1.1 1.8 2015 1.0 1.6 2016 1.3 1.3 2017 1.2 1.2 2018 1.3 1.7 2019 1.4 2.3NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 66. Step 1 of 2 : Suppose a sample of 251251 people is drawn. Of these people, 9595 passed out at G forces greater than 66. Using the data, estimate the proportion of people who pass out at more than 66 Gs. Enter your answer as a fraction or a decimal number rounded to three decimal places.1.- A study conducted in the automotive field states that more than 40% of vehicle engine failures are due to problems in the cooling system. To test this statement, a study is carried out on 70 vehicles and the critical region is defined as x < 26, where x is the number of vehicle engines that have problems in the cooling system. (use the normal approximation)a) Evaluate the probability of making a type I error, assuming that p = 0.4.b) Evaluate the probability of committing a type II error, for the alternative p = 0.3.
