Project
Sheet1 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 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. StatCrunch Data Set NOTE: Please see the set of data from Project #1 Question 1 (4 points) 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.) Calculate the probability of randomly selecting a vehicle with an engine size less than 2.7 L. enter your response here % (Round to two decimal places as needed.) Part 2 Calculate the probability of randomly selecting a vehicle with an engine size greater than 3.9 L. enter your response here % (Round to two decimal places as needed.) Part 3 Calculate the probability of randomly selecting a vehicle with an engine between than 3.1 L and 4.2 L. enter your response here % (Round to two decimal places as needed.) Part 4 Calculate the engine size that represents the 10th percentile of this sample. enter your response here L (Round to two decimal places as needed.) Question 2 (3 points) Agency leadership is very interested in trend analysis. Using the 750 randomly selected vehicles as their sample, data was 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? enter your response here % (Round to two decimal places as needed.) What is the 95% upper limit? enter your response here % (Round to two decimal places as needed.) 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 outside the constructed confidence interval. C. No, since 90% lies outside the constructed confidence interval. D. Yes, since 90% lies within the constructed confidence interval. Question 3 (10 points) 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? What is the appropriate null hypothesis in this case? The proportion of all vehicles that meet or exceed current fuel economy standards is _________ 90%. Please choose the most appropriate words to put in the above blank: A. equal to B. greater than C. not equal to D. less than What is the appropriate alternative hypothesis in this case? The proportion of all vehicles that meet or exceed current fuel economy standards is _________ 90% Please choose the most appropriate words to put in the above blank: A. equal to B. greater than C. not equal to D. less than What is the test statistic for this hypothesis test? The test statistic is enter your response here . (Round to two decimal places as needed.) . What is the p-value for this hypothesis test? The p-value is enter your response here (Round to three decimal places as needed.) What would you conclude based on an α = 0.05 level? We ___(1)____ the null hypothesis and _____(2)____ the alternative hypothesis since there ___(3)_____ sufficient evidence that the proportion of all vehicles that meet or exceed current fuel economy standards is ___(4)____ than 90% due to the p-value being __(5)______ than the α level. Please fill in the blanks above with the appropriate words. For (1), the choices are A. fail to reject B. reject For (2), the choices are A. accept B. do not accept For (3), the choices are A. is B. is not For (4), the choices are A. less B. greater For (5), the choices are A. greater B. less 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? Question 4 (4 points) 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. 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? enter your response here (Round to two decimal places as needed.) Part 2 What is the 95% upper limit? enter your response here (Round to two decimal places as needed.) Part 3 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 outside the constructed confidence interval. B. Yes, since 2500 lies within the constructed confidence interval. C. Yes, since 2500 lies outside the constructed confidence interval. D. No, since 2500 lies within the constructed confidence interval. Part 4 Explain why the agency would construct a confidence interval instead of collecting vehicle weight information of all passenger vehicles currently on the road. Question 5 (4 points) 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. 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? enter your response here (Round to two decimal places as needed.) Part 2 What is the 90% upper limit? enter your response here (Round to two decimal places as needed.) Part 3 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 interval. C. No, since 2400 lies within the constructed confidence interval. D. Yes, since 2400 lies outside the constructed confidence interval. Part 4 Compare your 90% confidence interval to the 95% confidence interval, (2484.92, 2569.56). Explain which confidence interval is wider and why. Question 6 (10 points) 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 _________ 2600 pounds Choices for the blank are A. equal to B. greater than C. not equal to D. less than What is the appropriate alternative hypothesis in this case? The mean vehicle weight of all passenger vehicles currently on the road is _________ 2600 pounds Choices for the blank are A. equal to B. greater than C. not equal to D. less than What is the test statistic for this hypothesis test? The test statistic is enter your response here . (Round to two decimal places as needed.) Part 5 What is the p-value for this hypothesis test? The p-value is enter your response here . (Round to three decimal places as needed.) What would you conclude based on an α = 0.05 level? We ___(1)____ the null hypothesis and _____(2)____ the alternative hypothesis since there ___(3)_____ sufficient evidence that the mean vehicle weight of all passenger vehicles currently on the road is ___(4)____ 2600 pounds due to the p-value being __(5)______ than the α level. Please fill in the blanks above with the appropriate words. For (1), the choices are A. fail to reject B. reject For (2), the choices are A. accept B. do not accept For (3), the choices are A. is B. is not For (4), the choices are A. equal to B. not equal to For (5), the choices are A. greater B. less