1 Byers and Williams (Viscosities of Binary and Ternary Mixtures of Polyaromatic Hydrocarbons," Journal of Chemical and Engineering Data, 32, 349 – 354, 1987) studied the impact of temperature (the regressor) on the viscosity (the response) of toluene- tetralin blends. The following table gives the data for blends with a 0.4 molar fraction of toluene. Temperature (°C) Viscosity (mPa·s) 1.133 24.9 35.0 0.9772 44.9 0.8532 55.1 0.7550 65.2 0.6723 75.2 0.6021 85.2 0.5420 95.2 0.5074 Plot a scatter diagram. Does it seem likely that a straight-line model will be adequate?
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- The article “Withdrawal Strength of Threaded Nails” (D. Rammer, S. Winistorfer, and D. Bender, Journal of Structural Engineering 2001:442–449) describes an experiment comparing the ultimate withdrawal strengths (in N/mm) for several types of nails. For an annularly threaded nail with shank diameter 3.76 mm driven into spruce-pine-fir lumber, the ultimate withdrawal strength was modeled as lognormal with μ = 3.82 and σ = 0.219. For a helically threaded nail under the same conditions, the strength was modeled as lognormal with μ = 3.47 and σ = 0.272. a) What is the mean withdrawal strength for annularly threaded nails? b) What is the mean withdrawal strength for helically threaded nails? c) For which type of nail is it more probable that the withdrawal strength will be greater than 50 N/mm? d) What is the probability that a helically threaded nail will have a greater withdrawal strength than the median for annularly threaded nails? e) An experiment is performed in which withdrawal…A study was conducted to examine if children with autism spectrum disorder (ASD) had higher prenatal exposure to air pollution, specifically particulate matter < 2.5 g in diameter (PM2.5). Researchers obtained birth records of all children born in Los Angeles between 2000 and 2008 and linked these to the Department of Developmental Services records to determine if any of those subjects had been diagnosed with ASD or not. They used the birth addresses given in the birth records to determine the average daily PM2.5 for the third trimester for each child. The standard deviation for PM2.5 among ASD subjects was found to be 34.6 and for non-ASD subjects was 16.8. Assume PM2.5 is normally distributed. 4a. What was the study design? * Randomized Clinical Trial (RCT) * Case Report * Nested Case-Control Study * Case-Control Study * cross-sectional study Cohort Study 4B. What are the null and alternative hypotheses? 4c. What type of statistical test would you use to analyze the…The article “Differences in Susceptibilities of Different Cell Lines to Bilirubin Damage” (K. Ngai, C. Yeung, and C. Leung, Journal of Paediatric Child Health, 2000:36–45) reports an investigation into the toxicity of bilirubin on several cell lines. Ten sets of human liver cells and 10 sets of mouse fibroblast cells were placed into solutions of bilirubin in albumin with a 1.4 bilirubin/albumin molar ratio for 24 hours. In the 10 sets of human liver cells, the average percentage of cells surviving was 53.9 with a standard deviation of 10.7. In the 10 sets of mouse fibroblast cells, the average percentage of cells surviving was 73.1 with a standard deviation of 9.1. Find a 98% confidence interval for the difference in survival percentages between the two cell lines.
- Q3. Kaimura et al. (2000) investigated the effects of procyanidin B-2 tonic on human hair growth after sequential use for 6 months. In one part of the study, the total hair increase (total hairs at month 6 – total hairs at month 0) in the designated scalp area was measured for a sample of 15 men treated with a placebo control and a sample of 25 men treated with a procyanidin B-2 (PB2). The data is contained in the file A2Q3.csv. (This data is simulated based on information in the paper. You must use the data in the file to carry out the analysis). Is there evidence that the total hair increase of the subjects in the procyanidin B-2 group was greater the those in the placebo control group, at the 5% level of significance? State an appropriate null and alternative hypothesis in words and symbols.A study carried out to investigate the distribution of totalbraking time (reaction time plus accelerator-to-brake movementtime, in ms) during real driving conditions at 60 km/hr gave the following summary information on the distributionof times (“A Field Study on Braking ResponsesDuring Driving,” Ergonomics, 1995: 1903–1910):mean 5 535 median 5 500 mode 5 500sd 5 96 minimum 5 220 maximum 5 9255th percentile 5 400 10th percentile 5 43090th percentile 5 640 95th percentile 5 720What can you conclude about the shape of a histogramof this data? Explain your reasoning.Test the hypothesis that the average weekly allowance of female and male ACC 215 students the same, at 5%l evel of significance. Weekly Allowance of Students (Php) Male: 1500 2000 2500 2500 2000 1750 2000 1800 Female:1500 2000 1750 1500 2000 2500 3000 3500 Ho: Ha: α = Decision Rule: Computation: Decision: Conclusion:
- Recent publications have addressed the growing concern in the scientific community around the increased prevalence of CAT scans in children between the ages of 7-18 and the growing rate of childhood cancers. Suppose the researcher plans to gather a SRS from a group of children in this age range who have received one or more CAT scans, and a SRS from a group of children who have never received a CAT scan and compare the number of cases of childhood cancers that develop over a prolonged period of time. Assume the following table summarizes the descriptive statistics for his samples. Population Average cases of childhood cancers Standard deviaton Sample size >CAT scan 24.6 2.4 1,894 No CAT scans 11.4 1.9 2,745 A) Carry out the appropriate statistical test to answer the researcher’s hypothesis regarding the difference in average cases of childhood cancers in children aged 7-18 receiving one or more CAT scans versus those that have never received a CAT scan. Use an alpha level…Suppose a researcher is interested inthe effectiveness in a new childhood exercise program implemented in a SRS of schools across a particular county. In order to test the hypothesis that the new program decreases BMI (Kg/m2), the researcher takes a SRS of children from schools where the program is employed and a SRS from schools that do not employ the program and compares the results. Assume the following table represents the SRSs of students and their BMIs. Student intervention group BMI (kg/m2) Student control group BMI (kg/m2) A 18.6 A 21.6 B 18.2 B 18.9 C 19.5 C 19.4 D 18.9 D 22.6 E 24.1 F 23.6 A) Assuming that all the necessary conditions are met (normality, independence, etc.) carry out the appropriate statistical test to determine if the new exercise program is effective. Use an alpha level of 0.05. Do not assume equal variances.B) Construct a 95% confidence interval about your estimate for the average difference in BMI between the groups.A cohort study is conducted to assess the association between clinical characteristics and the risk of stroke. The study involves n=1,250 participants who are free of stroke at the study start. Each participant is assessed at study start (baseline) and every year thereafter for five years. The following table displays data on hypertensive status measured at baseline and incident stroke over 5 years. Free of Stroke at 5 Years Stroke Baseline: Not Hypertensive 952 46 Baseline: Hypertensive 234 18 Compute the population attributable risk of stroke for patients with hypertension.
- A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms. Full data set Carpeted Uncarpeted 7.5 14.9 9.4 5.1 10.6 4.2 9.2 12.7 9.9 13.3 9.3 4.2 6.9 11.1 7.5 12.5 Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the α=0.05 level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers. State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms. A. H0: μ1=μ2 H1: μ1>μ2 This is the correct answer. B. H0: μ1<μ2 H1: μ1>μ2 C. H0: μ1=μ2 H1: μ1≠μ2 D. H0: μ1=μ2 H1: μ1<μ2 Your answer is not correct. Determine the P-value for this hypothesis test. P-value=nothing…Listed below are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample by baby teeth obtained from Pennsylvania residents and New York residents born after 1979. Use a 0.05 significance level and Wilcoxon rank-sum test to test the claim that the median amount of strontium-90 from Pennsylvania residents is the same as the median from New York residents. Pennsylvania 155 142 149 130 151 163 151 142 156 133 138 161 New York 133 140 142 131 134 129 128 140 140 140 137 143 1. what is the exact value of R = R 1 (Pennsylvania)? (Round off to 1 decimal place.) 2. what is the value of μ R ? (Type as a whole number.) 3. what is the value of σ R ? (Round off to 2 decimal places.) 4. what is the computed value of z ? (Round off to 2 decimal places.) 5. what is the tabular value of z ? (Round off to 2 decimal places.Seedlings of understory trees in mature tropical rainforests must survive and grow using inter- mittent flecks of sunlight. How does the length of exposure to these flecks of sunlight (fleck duration) affect growth? Leakey et al. (2005) experimentally irradiated seedlings of the Southeast Asian rainforest tree Shorea leprosula with flecks of light of varying duration while maintaining the same total irradiance to all the seedlings. Their data for 21 seedlings are listed in the following table. i. What is the rate of change in relative growth rate per minute of fleck duration? provide a standard error for your estimate. ii. using these data, test the hypothesis that fleck duration affects seedling growth rate. iii. Calculate a 99% confidence interval for the slope of the population regression.