(c) We want to test if there is a (positive) reduction in annual gas consumption provided by the extra insulation. Denote µx as the mean annual gas consumption for houses with standard insulation, and µy as the mean annual gas consumption for houses with extra insulation. (i) What are the null and alternative hypotheses?
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- The Specific Absorption Rate (SAR) for a cell phone measures the amount of radio frequency (RF) energy absorbed by the user's body when using the handset. Every cell phone emits RF energy. Different phone models have different SAR measures. To receive certification from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.5 watts per kilogram. A sample of 47 models was tested and the average of their Specific Absorption Rates (SARs) was found to be 1.18 watts per kilogram. Assume that the population standard deviation is 0.25 watts per kilogram. Construct a 90% confidence interval for the mean of the SARs for cell phones that received certification from FCC. Margin of error (if applicable): (Round the answer to 2 decimal places)The Specific Absorption Rate (SAR) for a cell phone measures the amount of radio frequency (RF) energy absorbed by the user's body when using the handset. Every cell phone emits RF energy. Different phone models have different SAR measures. To receive certification from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.5 watts per kilogram. A sample of 47 models was tested and the average of their Specific Absorption Rates (SARs) was found to be 1.18 watts per kilogram. Assume that the population standard deviation is 0.25 watts per kilogram. Construct a 90% confidence interval for the mean of the SARs for cell phones that received certification from FCC. Point estimate: =watts per kilogram (Round the answer to 2 decimal places) Confidence level % and �= , also �2= , and 1-�2= Critical values: (Round the answer to 2 decimal places) left= right=In a large scale study of energy conservation in single family homes, 20 homes were randomly selected from homes built in a housing development in southern England. Ten of the houses, randomly selected from the 20 houses selected for the study, were constructed with standard levels of insulation (70 mm of roof insulation and 50 mm of insulation in the walls). The other 10 houses were constructed with extra insulation (120 mm of roof insulation and 100 mm of insulation in the walls). Each house was heated with a gas furnace and energy consumption was monitored for eight years. The data shown below give annual gas consumption in MWh for each of the 20 houses. Standard Insulation Extra Insulation 13.8 15.1 17.8 13.9 18.0 15.9 17.3 17.2 16.9 15.2 19.9 13.8 13.6 11.3 17.6 13.2 15.9 18.8 12.3 14.0 Sample means Sample Standard Deviation 16.31 14.84 2.38 2.12
- The Specific Absorption Rate (SAR) for a cell phone measures the amount of radio frequency (RF) energy absorbed by the user's body when using the handset. Every cell phone emits RF energy. Different phone models have different SAR measures. To receive certification from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.5 watts per kilogram. A sample of 47 models was tested and the average of their Specific Absorption Rates (SARs) was found to be 1.18 watts per kilogram. Assume that the population standard deviation is 0.25 watts per kilogram. Construct a 90% confidence interval for the mean of the SARs for cell phones that received certification from FCC. Confidence interval:( , ) Interpretation: We are % confident that the mean of the SARs for cell phones that received certification from FCC is between watts per kilogram and watts per kilogram.The Specific Absorption Rate (SAR) for a cell phone measures the amount of radio frequency (RF) energy absorbed by the user’s body when using the handset. Every cell phone emits RF energy. Different phone models have different SAR measures. To receive certification from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.6 watts per kilogram. A random sample of 20 of the highest SAR level for a random selection of cell phone models as measured by the FCC was collected. Find a 96% confidence interval for the true (population) mean of the Specific Absorption Rates (SARs) for cell phones. Assume that the population standard deviation is σ = 0.337 and the sample mean is 1.024A study was conducted to examine the effect of diet cola consumption on calcium levels in women. A sample of 16 healthy women aged 18 to 40 were randomly assigned to drink 24 ounces of either diet cola or water. Their urine was collected for three hours after ingestion of the beverage and calcium excretion (in mg) was measured. The data are stored in ColaCalcium.
- A randomized experiment measured weight gain (in grams) of makes rats under six diets varyingby source of protein (beef, cereal, pork) and level of protein (low, high). Ten rats were assignedto each diet. Outline the design.Workers in the office like to drink coffee during work. A doctor is concerned about this situation since the too much coffee consumption may result to long-term health problems. However, studies suggests that there is no risk in drinking three cups of coffee per day, which is about 250 mg of caffeine. The doctor wants to know if the amount of caffeine consumed by the workers is within tolerable limits. He randomly selected 20 students and found that they consume an average of 270 mg of caffeine each day with a standard deviation of 48 mg. Assume that the daily amount of caffeine consumed by students follow the normal distribution.1. Which of the following sets of hypotheses should be used in this study? A. Ho: μ = 250 vs. Ha: μ > 250 B. Ho: μ ≤ 250 vs. Ha: μ > 250 C. Ho: μ = 270 vs. Ha: μ > 270 D. Ho: μ = 270 vs. Ha: μ ≠ 270 2. Which of the following is(are) TRUE? I. The appropriate test procedure to answer the objective of the study is a…Four different formulations of an industrial glue are being tested. Each of the different formulations were randomly applied to joint parts of five test specimen and the tensile strength of the glue when it is applied to each test specimen is recorded. However, the tensile strength is also related to the application thickness. The data on the strength (in lbs) and thickness (in 0.01 inches) are shown in the following table. Identify the treatment (specify levels), experimental units, concomitant variable, and response variable.
- As part of the United States Department of Agriculture's Super Dump Cleanup in the early 2000s, various sites in the country were targeted for cleanup. Three of the targeted sites - River X, River Y, and River Z - had become contaminated with pesticides because they were located near abandoned pesticide dump sites. Measurements of the concentration of aldrin (a commonly used pesticide) were taken at twenty randomly selected locations in each river near the dump sites. The boxplots shown below display the five-number summaries for the concentrations, in parts per million (ppm) of aldrin, for the twenty locations that were sampled in each of the three rivers. River X River Y River Z+ 3.4 (a) Compare the distributions of concentration of aldrin among the three rivers. Use your SOCS. (b) The twenty concentrations of aldrin for River X are given below. 4.0 5.6 5 6 7 Concentrations of Aldrin (ppm) 8.6 5.1 8.7 River X Aldrin Concentration Data 3.7 8.0 5.5 5.3 8 4.6 4.2 4.3 7.3 7.5 5.3 8.2 4.7…A traffic office in a country was in charge of a study where the safety of passengers in different types of cars was examined. Three models were examined; small cars, minivans and SUVS and six cars in each category were inspected. A special traffic accident simulator was used in the study and the pressure on the drivers' heads was measured. Umferðarastofa wanted to investigate whether there was a difference in the average pressure on the head during a collision in these three types of cars and used a variance analysis for this purpose. Failed to complete the square sum table, which can be seen below. weekend sum degree of freedom ave week sums between groups (area) 725.4 within groups (area) 178.6 XXX total Questions 1-3 deal with this study by the Traffic Authority. Question 1 What value should be given where xxx is in the table? 1 1.91 2. 2679 3. 3036.2 4. The information provided cannot be answered. Question 2 to be used to check if there is a difference in the average- What is the…The data given below are measurements (in micrometer units) of the thorax length of the aphid, Pemphigus populitransversus. The aphids were collected in 6 galls on the cottonwood, Populus deltoides. Four alate (winged) aphids were randomly selected from each gall and measured. The alate aphids of each gall are mostly isogenic (identical twins), being decended parthenogenetically from one stem mother. Thus, any variance within galls should be due to environment only. Variance among different galls may be due to differences in genotype and also to environmental differences among galls. Do a one-way ANOVA to test whether there significant intergall variance. Gall No. Replicate No. 1 2 3 4 5 6 1 4.4 5.7 6.2 5.1 6.1 6.2 2 4.9 5.1 5.1 6 6 6.2 3 4.7 5.8 6.1 5.8 5.7 5.3 4 4.8 5.5 5.3 5.9 6 6.3 Average 4.70 5.53 5.68 5.70 5.95 6.00 Ho: Ha: T stat: df: P: Conclusion relative to hypothesis