Not easy one ,problem set related to Statistics for Program Evaluationplease go through all the material make sure you can handle it before bidfirst doc file is the question and second pdf file is the related artical and third pdf file is the database for this problem set

ContextA high school student named David Merrell did an experiment to examine if music affects the ability of rats to run a maze. The explanatory variablewas exposure to music. He had three treatment groups: one group listened to heavy metal music by the group Anthrax. A second group listened to Mozart. The third group never heard music. This last group is the control group.The response variable was the average time (in seconds) to complete three runs. Every week the rats ran the maze three times. Merrell recorded each rat's average time for the week.Direct controls of potential confounding variables:Merrell trained all of the rats to run the same maze.He gave all mice the same amount of food and light.All mice had the same approximate age and weights.During the treatment phase, the rats were exposed to the treatment for the same amount of time, e.g. rats heard music at 70 decibels for 10 hours a day for a month.Results:By the end of the month the Anthrax group was much slower at running the maze. The Mozart group was much faster. The dotplots below show average run times for the first and last week of the experiment. Each dot represents one rat. The X-value is the rat’s average run time for the week. (Each rat ran the maze 3 times each week.) The blue line is the mean run time for each treatment group.If you are curious, here is a video of Merrell explaining his experiment.Merrell explaining his experiment (Links to an external site.)

A federal government agency that is responsible for setting vehicle fuel economy standards for automobile manufacturers is conducting research in order to update its fuel economy standards for the year 2030. Automobile manufacturers, and consumers, are highly interested in what the agency's findings and determinations will be as this will affect every vehicle in the United States. The federal government agency is very interested in the relationship between the weight of a vehicle and the vehicle's fuel economy (average miles per gallon (MPG)). Specifically, the agency is concerned that if the current trend of automobile manufacturers producing heavier new vehicles continues that its fuel economy targets will not be met. The agency's research department recently collected data for analysis in order to support the agency's upcoming discussion with the industry regarding its proposed 2030 fuel economy standards. The average MPG from a random sample of 750 vehicles was recently calculated by the agency. The research division also collected the vehicle weight of these 750 randomly sampled vehicles. The Vehicle Number, Type, Vehicle Weight, Average MPG, Fuel Tank Size (Gallons), Engine Size (Liters), and Meet or Not Meet Current Standards data were collected for these 750 vehicles. 1. Agency leadership is interested in analyzing the engine sizes of this sample of 750 vehicles. (Use the mean and standard deviation of the Engine Size (L) data. Also, if appropriate based upon your visual analysis of a histogram of the Engine Size (L) data, use the Normal distribution to answer this question.) ROUND TO TWO DECIMAL PLACES-Calculate the probability of randomly selecting a vehicle with an engine size less than 2.7 L.-Calculate the probability of randomly selecting a vehicle with an engine size greater than 3.9 L.-Calculate the probability of randomly selecting a vehicle with an engine between 3.1 L and 4.2 L.-Calculate the engine size that represents the 10th percentile of this sample.2. Agency leadership is very interested in trend analysis. Using the 750 randomly selected vehicles as their sample, data were collected to determine which vehicles currently meet or exceed fuel economy standards and which vehicles currently do not meet fuel economy standards. This information is found in the Meet or Not Meet Current Standards column. Agency leadership asks your team to construct a 95% One-Sample proportion confidence interval for the population proportion of all vehicles that meet current fuel economy standards. Assume that all necessary Central Limit Theorem conditions for a One-Proportion confidence interval have been met.-What is the 95% lower limit?-What is the 95% upper limit?-Using the 95% confidence interval, would it be plausible to conclude that the population proportion of vehicles that currently meet fuel economy standards is 90%?A. No, since 90% lies within the constructed confidence interval.B. Yes, since 90% lies within the constructed confidence interval.C. No, since 90% lies outside the constructed confidence interval.D. Yes, since 90% lies outside the constructed confidence interval.3. Agency leadership decides to run a One Proportion hypothesis test to determine if the proportion of all vehicles that meet or exceed current fuel economy standards is less than 90%. Assume that all necessary Central Limit Theorem conditions for a One-Proportion Z-test have been met.-What is the appropriate null hypothesis in this case? The proportion of all vehicles that meet or exceed current fuel economy standards is, less than, not equal to, greater than, or equal to, 90%.-What is the appropriate alternative hypothesis in this case? The proportion of all vehicles that meet or exceed current fuel economy standards is, less than, greater than, not equal to, or equal to, 90%.-What is the test statistic for this hypothesis test? The test statistic is-What is the p-value for this hypothesis test? The p-value is-What would you conclude based on an α=0.05 level?We, fail to reject or reject, the null hypothesis and, do not accept or accept, the alternative hypothesis since there,is not or is, sufficient evidence that the proportion of all vehicles that meet or exceed current fuel economy standards is, greater or less, than 90% due to the p-value being, greater or less, than the α level.-Explain the results of your hypothesis test. What does the p-value signify? Would you say the observed outcome was unusual? If so, how unusual was the outcome?4. Agency leadership decides to use the vehicle weight data from its random sample of 750 vehicles to estimate the mean vehicle weight of all passenger vehicles currently on the road. Construct a 95% One-Sample T confidence interval for the mean vehicle weight of all passenger vehicles currently on the road. Assume that all necessary Central Limit Theorem conditions for a One-Sample T confidence interval have been met.-What is the 95% lower limit?-What is the 95% upper limit?- Using the 95% confidence interval, would it be plausible to conclude that the mean vehicle weight of all passenger vehicles currently on the road is 2500 pounds?A. No, since 2500 lies within the constructed confidence intervalB. Yes, since 2500 lies outside the constructed confidence interval.C. Yes, since 2500 lies within the constructed confidence interval.D. No, since 2500 lies outside the constructed confidence interval.-Explain why the agency would construct a confidence interval instead of collecting vehicle weight information of all passenger vehicles currently on the road.5. Agency leadership decides to use the vehicle weight data from its random sample of 750 vehicles to estimate the mean vehicle weight of all passenger vehicles currently on the road. Construct a 90% One-Sample T confidence interval for the mean vehicle weight of all passenger vehicles currently on the road. Assume that all necessary Central Limit Theorem conditions for a One-Sample T confidence interval have been met.-What is the 90% lower limit?-What is the 90% upper limit?-Using the 90% confidence interval, would it be plausible to conclude that the mean vehicle weight of all passenger vehicles currently on the road is 2400 pounds?A. No, since 2400 lies outside the constructed confidence interval.B. Yes, since 2400 lies within the constructed confidence intervalC. Yes, since 2400 lies outside the constructed confidence interval.D. No, since 2400 lies within the constructed confidence interval.-Compare your 90% confidence interval to the 95% confidence interval, (2484.92, 2569.56). Explain which confidence interval is wider and why.6. Agency leadership decides to run a One Sample-T hypothesis test to determine if the mean vehicle weight of all passenger vehicles currently on the road is significantly different than 2600 pounds. Assume that all necessary Central Limit Theorem conditions for a One-Sample T-test have been met.-What is the appropriate null hypothesis in this case? The mean vehicle weight of all passenger vehicles currently on the road is, less than, greater than, or equal to, 2600 pounds.-What is the appropriate alternative hypothesis in this case? The mean vehicle weight of all passenger vehicles currently on the road is, greater than, not equal to, equal to, or less than, 2600 pounds.-What is the test statistic for this hypothesis test? The test statistic is-What is the p-value for this hypothesis test? The p-value is-What would you conclude based on an α=0.05 level? We, reject or fail to reject, the null hypothesis and, accept or do not accept, the alternative hypothesis since there, is or is not, sufficient evidence that the mean vehicle weight of all passenger vehicles currently on the road is, not equal to or equal to, 2600 pounds due to the p-value being, greater or less, than the α level.-Based upon your hypothesis test, was the observed outcome unusual? If so, how unusual was the outcome?