Question

Reliance on solid biomass fuel for cooking and heating exposes many children from developing countries to high levels of indoor air pollution. An article presented information on various pulmonary characteristics in samples of children whose households in India used eithe biomass fuel or queried petroleum gas (LPG). For the 754 children in biomass households, the sample mean peak expiratory flow (a person's maximum speed of expiration) was 3.5 L/s, and the sample standard deviation was 1.2. For the 759 children whose households used liquefied petroleum gas, the sample maan PEF was 4.45 and the sample standard deviation was 1.51. (a) Calculate a confidence interval at the 95% confidence level for the population mean PEF for children in biomass households and then do likewise for children in LPG households. (Round your answers to two decimal places.) biomass households 0 .21 LPG households What is the simultaneous confidence level for the two intervals? (Round your answer to two decimal places.) (b) Carry out a test of hypatheses at significance level 0.01 to decide whether true average PEF is lawer for children in biomass households than it is for children in LPG households (the article included a P-value for this test). (Round your test statistic to two decimal places and your p-value to four decimal places. State the relevant hypotheses O Hobromass - MLPG - namas - Purco Ho: "biomass - MLPG - 0 4, blomss - Plec0 Ho: "biomass - MLPG = 0 Mo: Ablomss -LFC+ No: "bomass - MLPG = 0 M, blomss - LFG Ho: Momass - MLPG = 0 M: biomass - LFG 20 Calculate the test statistic and P-value. (Round your best statistic to two decimal places and your P-value to three decimal places.) P-value - State the conclusion in the problem context. Reject Hg. The data suggests that the true average PEF is lower for children in biomass households than it is for children in LPG households. Fell to relect Mo. The data does not suggest that the true average PEF is lower for children in biomass households than it is for children in LPG households. Reject Hg. The data does not suggest that the true average PEF is lower for children in blomass households than it is for children in LPG households. Fail to reject Mo. The data suggests that the true average PEF is lower for children in biomass households than it is for children in LPG households. (C) FEV,, the forced expiratory volume in 1 second, is another measure or pulmonary function. The cited article reported that for the biomass households the sample mean FEV, was 2.5 L/s and the sample standard deviation was 0.5 Vs. If this information is used to compute a 95% CI for population mean FEV, would the simultaneous confidence level for this interval and the first interval calculated in (a) be the same as the simultaneous confidence level determined there? Explain. 10 --Select--- . The two confidence intervals in (a) were from two 11 --Select-- random samples, and so the confidence levels could be multiplied: 12 ---Select- 3. However, two variables (PEF and FEV) collected on the saire group of 754 children 1a --Select-- constitute independent random samples. Hence, we 14 --Select-- say that the two resulting Cis for that population have the same simultaneous confidence level found in part (a).

Answer 1

Cimen data, sample size ni = 154 sample mean t = 35 standard deviation s, 11.2 and sample side ng = 159 Į - 4.46 sy - 1.51 a) Conferdance Inbrao s 95%. as in Confidence Q = 1-0.95 -0.05 1. The critical value of zal2 = 20.05/2 = 20.025 = 1.96 → 95% CI for the population mean PEF of for children in Biomass households ; es ā, † 2.elax (slam) = 3.5+ 1.96 ( 12/0754 ) = 3.5 0.086 CI= (3.41, 3.59) Biomass houlds ; (3.ul, 3.59) > 95% CI for the population mean pef for children in liquefied:

CI = 7, + Zelex (slo) 4.46 1.96 (15! (1759) = 4.46 $ 0.1074 cs (.35, 4.5+) 48 houeholds : (1:35, 4.57) The simultaneous Confidence Intence → for two intervals is 0.95%0.95 ; = 0.9025 90.254. b) Significance level N = 0.01 The noll and alterative hypothesis are all and Ho: Mbiomass - LG =0 Ha a biomass - elpa co - MLPG LO Coption B is Conect) → Test statistic! 2.*** (ats medle) S

- 35-6046-(0) - t 1.512 V 754 759 Z = -0.96 0.0701 Z - - 13.69 p-value : This is lept failed test p-value = p (222) =P (25 -13.69) p-value = 0.000 Conclusion! S p-value is less than significance level. so, we reject null hypothesis. O option a is Conect. n = 754 C) The no. of children in Biomass households mean Trev = 25 and Spev = 0.5 954. Simultaneous CI for the populakon - Refev + zole ( Selva FEU mean

* 5#196 (05/J7su) : 2.50.0357 CI = ( 206, 258) → No the two Confidence Internas in (a) were two independent random samples and the simultaneous Confidence level is 90.254. The two variables PEU and FEV Collected on the same groop of 754 childuen does not constitute independent random I samples. Hence, we can't say that two Confidence Intewas for the Whoo have the same inolteenous Confidence level in part (a) 1 population