(a) Does the size of the orifice affect the mean percentage of radon released? Use a =0.05. (b) Find a 95% confidence interval on the mean percent of radon released when the orifice diameter is 1.40.
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- Fluoride Exposure in Drinking Water Exercise 2.250 introduces a study showing that fluoride exposure might have long-term negative consequences for the offspring of pregnant women. Part of the study examines the effect of adding fluoride to tap water on mean fluoride concentration in women. Summary statistics for fluoride concentration (measured in mg/L) for the two groups are given in the table below. Tap water Fluoridated Non-fluoridated Conclusion: Sample size 141 228 Mean 0.69 0.40 St.Dev. 0.42 0.27 Find and interpret a 99% confidence interval for the mean increase in fluoride concentration for those with fluoridated tap water. Let Group 1 represent those with fluoridated tap water and Group 2 represent those without fluoridated tap water. Confidence interval: i to i (round to three decimal places)Each year the US Environmental Protection Agency (EPA) releases fuel economy data on cars manufactured in that year. Below are summary statistics on fuel efficiency (in miles/gallon for city driving) from random samples of cars with manual and automatic transmissions manufactured in 2012. We want to know if there is a statistical difference between the average fuel efficiencies between the two different types of transmission. Automatic Transmission Manual Transmission X1 = 15.7 Si = 3.6 N1 = 26 T2 = 19 S2 = 4.65 N2 = 34 Mean %3D SD Sample Size (a) Calculate the standard error for the appropriate sampling distribution: SE = (b) We want to calculate a 91% confidence interval for the difference between the gas mileages for the automatic transmission and the manual transmission cars. What is the critical t-score that we should use to build our confidence interval? tcritical (c) Calculate the margin of error, the lower bound, and the upper bound for the 91% confidence interval. Margin of…A researcher conducts a two-year study comparing the number of cavities in a group of 30 randomly selected young children from the community before and after the application of fluoride to test if there is a decrease in the number of cavities. This is an example of a/an: Independent-samples t test or Dependent-samples t test?
- The following statement appeared on a box of Tide laundry detergent: “Individual packages of Tide may weigh slightly more or less than the marked weight due to normal variations incurred with high speed packaging machines, but each day’s production of Tide will average slightly above the marked weight.” (d) Propose procedures to collect data to test the statement.using monthly data from January 1992 to December 2000, we estimate the following equation for lightweight vehicle sales: Δln (Salest) = 2.7108 + 0.3987Δln (Salest −1) + εt. table 5 gives sample autocorrelations of the errors from this model. table 5 lag 1 2 3 4 5 6 7 8 9 10 11 12 Different Order autocorrelations of Differences in the logs of vehicle Sales autocorrelation 0.9358 0.8565 0.8083 0.7723 0.7476 0.7326 0.6941 0.6353 0.5867 0.5378 0.4745 0.4217 Standard error 0.0962 0.0962 0.0962 0.0962 0.0962 0.0962 0.0962 0.0962 0.0962 0.0962 0.0962 0.0962 t-Statistic 9.7247 8.9005 8.4001 8.0257 7.7696 7.6137 7.2138 6.6025 6.0968 5.5892 4.9315 4.3827 a. use the information in the table to assess the appropriateness of the specification given by the equation. b. if the residuals from the ar(1) model above violate a regression assumption, how would you modify the ar(1) specification?Riboflavin (Vitamin B2) is determined in a cereal sample by measuring its fluorescence intensity(형광세기) in 5% acetic acid solution. A calibration curve was prepared by measuring the fluorescence intensities of a series of standards of increasing concentrations. The following data were obtained. Riboflavin (μg/mL) 0.000 0.100 0.200 0.400 0.800 Unknown sample Fluorescence intensity 0.0 5.8 12.2 22.3 43.3 15.4 (a) Use the method of least squares to obtain the best straight line through these five points (n=5). (b) Make a graph showing the experimental data and the calculated straight line. (c) An unknown sample gave an observed fluorescence intensity of 15.4. Calculate the concentration of Riboflavin (Vitamin B2) in the unknown sample (μg/mL). (d) Calculate the coefficient of determination (R2).
- Urinary fluoride concentration (in parts per million) was measured for both a sample of livestock that had been grazing in an area previously exposed to fluoride pollution and a similar sample of livestock that had grazed in an unpolluted region. Do the accompanying data indicate strongly that the mean fluoride concentration for livestock grazing in the polluted region is larger than that for livestock grazing in the unpolluted region? Assume that the distributions of urinary fluoride concentration for both grazing areas have the same shape and spread. Use a significance level of 0.05. Group 1 (Polluted): 21.3 || 18.7 || 23.0 || 17.1 || 16.8 || 20.9 || 19.7 Group 2 (Unpolluted): 14.2 || 18.3 || 17.2 || 18.4 || 20.0 What is/are the Mann-Whitney Rank Sum critical value(s) for this problem? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a 43 b 56 n 58,33 d 60An article reported data from a study in which both a baseline gasoline mixture and a reformulated gasoline were used. Consider the following observations on age (yr) and NOx emissions (g/kWh): Engine 1 2 3 4 5 6 7 8 9 10 Age 0 0 2 11 7 16 9 0 12 4 Baseline 1.74 4.38 4.04 1.23 5.30 0.58 3.35 3.44 0.73 1.23 Reformulated 1.85 5.93 5.52 2.67 6.54 0.76 4.94 4.87 0.69 1.39 Construct scatter plots of the baseline NOx emissions versus age. Construct scatter plots of the reformulated NOx emissions versus age. What appears to be the nature of the relationship between these two variables? As age increases, emissions also increase.As age increases, emissions decrease. There is no compelling relationship between the data.Please show your work. Thank you.An experiment was conducted to investigate the effects of the concentrations of sulfuric acid (H2SO4) and calcium chloride (CaCl2) on the amount of black mud precipitate in the treatment of alkaline wastewater. There were three levels of each concentration, and two replicates of the experiment were made at each combination of levels. The relevant statistical analysis is provided in the following table: (image) a) Does there appear to be an interaction between concentration of sulfuric acid and calcium chloride at the .05 level? What does this say about the additive model? b) Can the effect of concentration of sulfuric acid on amount of black mud precipitate in the treatment of alkaline wastewater be described by interpreting the main effects of concentration of sulfuric acid? If so, interpret the main effects at the .05 level, including the appropriate test statistic and p-value. If not, explain why not.c) Can the effect of concentration of calcium…
- Hotel prices worldwide are projected to increase by 3% next year (Lodging Magazine website, June 15, 2016), but is there a difference between Europe and the U.S.? Suppose we have projected changes in hotel costs for 47 randomly selected major European cities and 53 randomly selected major U.S. cities. These data are provided in the DATAfile IntHotels. Use α= .01 What is the p-value?.What is your conclusion?(d) Calculate the value of a test statistic: z* for Table 3, or U* for Table 13 (your choice). (f) What conclusion do you reach about the null hypothesis? Justify.Auto noise filters In a statement to a Senate Public WorksCommittee, a senior executive of Texaco, Inc., cited astudy on the effectiveness of auto filters on reducing noise. Because of concerns about performance, two types of fil-ters were studied, a standard silencer and a new device developed by the Associated Octel Company. Here are theboxplots from the data on noise reduction (in decibels) ofthe two filters. Type 1 = standard; Type 2 = Octel. ANOVA Table Source DFSum ofSquaresMeanSquare F-Ratio P-ValueType 1 6.31 6.31 0.7673 0.3874Error 33 271.47 8.22Total 34 2.77Means and Std DeviationsLevel n Mean StdDevStandard 18 81.5556 3.2166Octel 17 80.7059 2.43708a) What are the null and alternative hypotheses?b) What do you conclude from the ANOVA table?c) Do the assumptions for the test seem to be reasonable?d) Perform a two-sample pooled t-test of the difference.What P-value do you get? Show that the square of thet-statistic is the same (to rounding error) as the F-ratio.