Congress regulates corporate fuel economy and sets an annual gas mileage for car
ID: 3231682 • Letter: C
Question
Congress regulates corporate fuel economy and sets an annual gas mileage for cars. A company with a large fleet of cars hopes to meet the goal of 34.6 mpg or better for their fleet of cars. To see if the goal is being met, they check the gasoline usage for 32 company trips chosen at random, finding a mean of 36.60 mpg and a standard deviation of 5.36 mpg. Is this strong evidence that they have attained their fuel economy goal? Complete parts (a) through (f) below. Use 0.05 as the P-value cutoff level.
a) Write appropriate hypotheses. e mean fuel economy of all cars in the company's fleet is denoted by H) O A. Ho u 34.6 HA: 34.6 O B. Ho: 34.6 HA: H 34.6 O C. Ho: 34.6 HA: 34.6 O D. Ho: 34.6 HA: 34.6 b) Are the necessary assumptions to make inferences satisfied? Choose the correct answer below. O A. The company uses a random sample, so assume the population follows a Student's t-model one can assume the data are dependent. If the sample size is less than 10% of the population, and there are at least 10 successes and 10 failures, one can O B. The company uses a random sample, so one can assume the data are independent. If the sample size is less than 10% of the population, and there are at least 10 successes and 10 failures, one can assume the population follows a Student's t-model O C. The company uses a random sample, so one can assume the data are independent. If there are no outliers, and the data are unimodal, symmetric, and only mildly skewed. one can assume the data come from a Normal population O D. The company uses a random sample, so one can assume the data are dependent If there are no outliers, and the data are unimodal, symmetric, and only mildly skewed, one can assume the data come from a Normal population c) Describe the sampling distribution model of mean fuel economy for samples like this. Choose the correct answer below. y 34.6 O A. 31 s 32 34.6 31 5.36 y O C. 34.6 31 5.36 y 34.6 /SE (y) d) F nd the P-value. P-value (Round to three decimal places as needed.) e) Explain what the P-value means in this context, Choose the comect answer belo O A. The probability of observing a sample mean higher than 34.6 is 2.1%. assuming the data come from a population that follows a Nomal model O B. The probability of observing a sample mean lower than 36.60 is 2.1%, assuming the data come from a population that follows a Normal model O C. If the average fuel economy is 36.60 mpg, the chance of obtaining a population mean of 34.6 or more by natural sampling variation is 2.1% O D. If the average fuel economy is 34.6 mpg, the chance of obtaining a sample mean of 36.60 or more by natural sampling variation is 2.1%. f) State an appropriate conclusion. Choose the comect answer below. O A. Reject the null hypothesis. There is strong evidence that the company is meeting their goal O B. Reject the null hypothesis. There is not strong evidence that the company is meeting their goal O C. Fail to reject the null hypothesis. There is strong evidence that the company is meeting their goal O D. Fail to reject the null hypothesis. There is not strong evidence that the company is meeting their goalExplanation / Answer
a)option B is correct
b)option C is correct
c)option A is correct
d)here std error=std deviation/(n)1/2 =0.9475
hence test stat t=(X-mean)/std error =2.1108
p value=0.021
e)option D is correct
f)option A is correct